Judgement is assuring each individual gets what is due to him so it does require sound reasoning but it also requires the authority to then give what is due.

You're talking more about executive decisions than judicial decisions.

If my neighbors are in an incestual relationship I can use reasoning to say that it is immoral but I cannot give them what is due, namely some sort of punishment.

Right, because their punishment is not your responsibility. That is society's responsibility. To rightly punish someone, you need some executive authority, which you get by having society delegate it to you.

And in fact we have no authorities who can give them what is due for their immorality.

Our society, at this point in its history, has decided not to punish incest in any formal way beyond prohibiting incestuous marriages. That doesn't mean we don't have informal ways of deterring it.

There is an idea going around that whatever is not prohibited by law is morally acceptable. It is way too widely accepted, but not nearly universally. Lots of people still know better, and I'm pretty sure they're in the majority.

Judgement is assuring each individual gets what is due to him so it does require sound reasoning but it also requires the authority to then give what is due. If my neighbors are in an incestual relationship I can use reasoning to say that it is immoral but I cannot give them what is due, namely some sort of punishment. And in fact we have no authorities who can give them what is due for their immorality.
Who has that authority in this case?

but that is not the authority to make valid judgements.

Judgments are not validated by authority. They are validated by sound reasoning.

There is no doubting the fact that we all have authority to make opinions but that is not the authority to make valid judgements.
In our society (western civilization) who has been delegated the authority to compel others to not engage in an incestual relationship?

Each of us has all the authority we need to have an opinion about whether a particular behavior is right or wrong. Every society delegates, to some of its members, the authority to compel others to comply with such opinions.

I don't like to discuss incest but was using it as an example of immorality that would deserve to be judged but lacks an authoritative judge.

I don't think anyone claims to have the authority.

Are we now talking just about incest? I thought we were talking about morality in general.

I don't think anyone claims to have the authority. Marriage licenses can be denied but that cannot stop it. Society can disapprove but that doesn't represent answering to authority.

I'll skip ahead to my conclusion, only God has the authority to judge immoral behavior (other than those that are regulated by the state such as murder, etc...), and He is the only one with authority to justly punish.

I'll try to back it up with justice logic if you're interested in voicing your objections.

Do you think nobody is exercising such power or authority now?

"That depends on how much power the one passing judgment has over those they judge."
That's my basic question, who would have power or authority to judge whether an incestual action deserves judgement and consequences?