"With respect philosophy is full of irrelevance when it comes to how the universe works." I don't disagree. But when it comes to teleological "why" questions science is full of irrelevance. So when you rephrased the question the philosopher asks with a question the scientist asks you've presupposed your answer is a scientific and not a philosophical question.

"For pity's sake respect an expert's opinion in their field EVEN if you don't like it." This is a bad take. First, experts in science should welcome challenging their conclusions because science embraces the fallibility of it's theories. Also, the posit of a brute fact is a philosophical question, not a scientific one. Science presupposes the principle of causality and positing something has no cause is a brute claim contrary to the entire enterprise of science. Many scientists do amateur philosophy and Sean Carrol is making an amateur philosophical claim not an expert scientific claim.

"does accepting the universe MUST have a cause inevitably lead you to the God," What other explanations besides the God of classic theism are you positing?

"Ignorance begets ignorance, Millennia after millennia of navel gazing did not change the world, the scientific method in 360+ years has!" Science cannot answer teleological why question or qualitative data questions that humans seek answers for. Equivocating non-scientific questions with naval gazing is an intellectually contemptuous approach. Passing it off as intellectually superior is ignorance begetting itself.

At the bottom, the Universe is indeed a brute fact.

Paramenides, "Nothing comes from nothing. So something has always existed."

Now the argument is what is that something? Parmenides "Is that something one thing or many things?" So far, as physics has progressed, it looks like that something, the brute facts of the Universe are physics and are many things. Energy, time, dimension, fields. the quantum foam. Virtual particles. The brute facts of the Universe. Exact nature unknown at this time.

God(s) have too many problems to be taken seriously. Problem of evil, problem of free will, God and logic, God and Time, theological fatalism. And has never really explained anything or lead to progress in understand the physical Universe.

Hmm theoretical physicist says "Yes"; philosopher thinks Not. Let me think, who knows more about the universe?

Which one to go with? Who knows best?

How about "Is Judy Garland's version of 'Somewhere Over the Rainbow' in the key of C Major?"

Musicologist says "yes"; Astrophysicist says, "Rainbows don't really exist, they are just sunlight refracted by rain droplets into different wave lengths and some of those wavelengths excite the photoreceptors in our retinas, causing their perception. I have no knowledge of a Judy Garland, Keys, C's or Majors.

With respect philosophy is full of irrelevance when it comes to how the universe works. Theoretical physicist do nothing else but obsess about universe, matter, time, fields, space, quanta, etc.

A Brute fact is a fact that has no explanation. An Epistemological brute fact is a brute fact who explanation is unknown. A metaphysical brute fact is a fact with no explanation because there isn't one even in principle.

Unless one learns this distinction arguing about it with Theists is a waste of time. When we say the universe can't be a brute fact we are talking about a metaphysical brute fact not an epistemological one.

First, I find it interesting how it’s permitted for an atheist to appeal to unintelligible brute facts but not the theist. If a theist were to say, “God is just a brute fact, there is no rhyme or reason to his existence,” then an atheist would feel justified in denying him membership among the intelligentsia

The theist can't say god is a brute fact because it isn't a fact that god exists. See, brute facts have to refer to things that are facts.

The Facts of Ordinary Life

So, why should an appeal to a brute fact when faced with the existence of the universe be reasonable when an appeal to a brute fact when faced with a dead body is not?

Because the laws of physics tell us that things within the universe follow a set of rules, and those rules say things will happen for reasons. The universe itself is not like anything in the universe, and logically, brute facts are unavoidable, even if you posit a god exists.

Can’t Get Out of the Taxi

Besides the fact this objection begs the question against the theist—if God exists then the universe would have an explanation for its existence—it commits what some philosophers have aptly called the “taxicab fallacy”; thus a third argument against the brute fact view. Why commit to the idea “Whatever exists has a reason for its existence” and then dismiss it like you dismiss a taxicab once you arrive at the universe as a whole? Such a move is arbitrary and thus unreasonable.

But there won't be a necessary explanation for why god created this particular universe, since it isn't necessary that god create this universe. And that means there's only a contingent explanation, and that leads to a dilemma. That dilemma is that once you take out necessary explanations your only 2 options are an infinite regress of contingent explanations or a brute fact. Saying god is a necessary being doesn't avoid the dilemma. God is his will, and god's will to create this universe isn't necessary. So god's will, and therefore essence is at least in part not necessary.

Logic also demands that eventually one must come to a brute fact, even if god exists. So the taxicab fallacy is itself a fallacy.

Skepticism of the Senses

For example, according to this line of reasoning there might be no connection between your experience of reading this article on a computer and the actual article the computer is showing on its monitor. Your experience might just be a brute fact having nothing to do with any of the objective things with which we normally would associate your experience.

We have positive reasons why this is not the case: the laws of physics. So there's not reason to think our senses are the result of brute facts.

No Arguments Allowed

The last argument I’ll offer for consideration comes from philosopher Edward Feser in his book Scholastic Metaphysics: A Contemporary Introduction. Feser argues the denial of the principle of sufficient reason is at the same time a denial of rational argumentation, including any argument for brute facts.
[...]
But if brute facts are possible, and the principle of sufficient reason is false, then it follows that our conclusion “Socrates is mortal” might have nothing to do with the truth of the premises and their logical structure.
[...]
The bottom line is, if brute facts are possible, there might be no reason whatsoever we believe what we do, even the belief that we believe on rational grounds.

Not at all. Because we have good reasons why things in the universe have explanations. Furthermore, logic forces us to confront the reality of brute facts. The Münchhausen trilemma assures that.

Conclusion

Sean Carroll is a brilliant man. He is courageous in taking on heavyweights of the likes of Dr. William Lane Craig. But why such a great mind can’t see the rational implications of denying the principle of sufficient reason, I do not know

I know. It's because your "rational implications" are false.

There is a famous trilemma in philosophy called the Münchhausen trilemma which states there are only three options when providing an explanation or proof of a given situation:

The circular argument, in which theory and proof support each other
The regressive argument, in which each proof requires a further proof, ad infinitum
The axiomatic argument, which rests on accepted precepts

When explaining something and you go down the line of the explanatory chain you will eventually have to resort on one of these three methods. Either your explanation will be circular, it will require an additional explanation ad infinitum, or it will terminate in an axiom which itself has no further explanation. This is identical to a brute fact, the only one that doesn't lead to absurdity. Now the theist will likely claim here that they have an argument that shows their god is logically necessary. But consider this. The traditional notion of god in classical theism is that of a timeless, changeless, immaterial mind, who also must be infinitely good, infinitely wise, and can do anything logically possible. This last point is important because we must establish that god cannot transcend logic. For example, god cannot create a rock too heavy for him to lift if he's omnipotent. That would be logically impossible.

The Münchhausen trilemma, show that brute facts not only make sense, they're unavoidable even if we posit god. Thus we could argue more formally:

The traditional notion of god in classical theism is that of a timeless, changeless, immaterial mind, who also must be infinitely good, infinitely wise, and can do anything logically possible.
All of god's will and desires must exist timelessly and eternally in an unchanging, frozen state.
That would mean that god timelessly and eternally had the desire to create our particular universe, and not some other universe, or no universe.
Our universe is not logically necessary; it didn't have to exist, and god didn't have to create it.
The theist would have to show that it was logically necessary for god to create our particular universe in order to avoid eventually coming to a brute fact.
There is no way to answer this question, even in principle, with something logically necessary.
Thus at least one brute fact must exist even if god exists.

"you cannot conceive of an effect without a cause."
Effect: a radioactive atom decaying at moment X, not at moment Y.
Cause: none according to Quantum Mechanics.
Thanks for confirming that you reject Modern Physics.

"the conclusion of deductive reasoning that starts with certain features of the world—motion (change), efficient causality, contingency, degrees of being, and final causality."

leads to circularity.

1. Features: motion (change), efficient causality, contingency, degrees of being, and final causality.
2. Conclusion: god is the first cause is not a brute fact.
3. God causes those features.
4. Back to 1.

Dawkin's point is that we still just as well can replace "god" by "the Universe". Of course Russell explains it much better in his History of the Western World. As I'm too lazy to look it up I paraphraze: when you search for causes you must begin at some point. You must accept one cause and stop asking what its cause was. And we're back at where we began: will we stop at "The Universe" or at "God"? And why?
Nothing in your article addresses that.

But it still gets worse for you.

Modern Physics is probabilistic. It postulates that there is no cause for a radioactive atom decaying (which is a change) at moment X instead of Y. It postulates that there is only a probability for that radioactive atom decaying in a given time interval. It postulates that that is the core feature of our Universe.
If "God created our Universe" (whatever "to create means" - apologists are remarkably vague about this) is to be consistent with Modern Physics then god is a gambling god. Anyone who thinks the Cosmological Argument a valid one should reconvert to pastafarianism (the only religion which is OK with a gambling creator) or admit that he/she rejects Modern Science.

One ultimate explanation of our Universe proposed by Modern Physics (it's my favouorite) is quantum fields.

http://plato.stanford.edu/entries/quantum-field-theory/

It seems to correctly describe how come that there is a Universe - ie it offers an explanation. Of course its totally probabilistic.
Here we're back at where we started: should we stop here or should we take one further step and postulate "God created quantum fields"? There is a Bible reference for the latter. "Let there be light" can be interpreted this way as photons are the bearers of light, the photon is one of the elementary particles and hence have there own quantum field. "Let there be light" becomes "Let there be the quantum field that accurately describes photons".
Quantum fields attach probabilities to all points in spacetime. So a god who created those quantum fields is a gambling god. This is the only way to formulate the Cosmological Argument in a way that's consistent with this concept.
Are you going to reject a scientific concept because philosophy? You would stand in a proud tradition of smart people making this very error.

I get it now. Thanks for your patience.