I think it means not a member of a religion or religious institution. So, an overarching category of "spiritual but not religious", agnostics, and atheists

1) Reality consists of the material world and its various interactions.
2) The material world and its various interactions are observable and knowable.
3) Therefore reality is observable and knowable.
4) Scientific experiments are conducted to observe and know the interactions of the material world.
5) To know an interaction of the material world is to have knowledge of reality.
6) Therefore knowledge of reality is determined via scientific experimentation.
7) In scientific experimentation, an observed interaction is modeled by some relationship of parameters thought to be influential.
8) The confidence level quantifies how well the model predicts future interactions.
9) Therefore the relationship (and quantity) of the parameters affects the confidence level.
10) A 100% confidence level must be achieved for knowledge of reality to be indisputable.
11) Experimental models do not achieve a 100% confidence level.
12) Therefore knowledge of reality is necessarily disputable.
13) If knowledge of reality is necessarily disputable,
14) then reality can never be known with absolute certainty.
15) Therefore one does not have absolute knowledge of reality, rather one has knowledge of how well an experimental model represents reality.

A few posts above this, 42Oolon wrote,

I do not think anyone expects certainty. Science certainly does not, nor does religion, love, the courts or any other pursuit

However, here BenS has written, "Your 'elementary reasoning' can only be used when you know, to a decent confidence level..."

As I try to piece together the reasons to prefer the atheist worldview as described by the atheist interlocutors, these statements are a contradiction because "a decent confidence level" is a claim of how much certainty one has regarding particular knowledge. In other words, 42Oolon was certain that science does not expect certainty, yet BenS says science expects a particular confidence level (without which the knowledge of a thing will not be certain enough.)

In this case, it would help to describe exactly what is "a decent confidence level," and how could one arrive at such a conclusion by way of scientific experiment (an experiment which presumably has results that are subject to yet another "decent" confidence level.) Do you agree that the challenge in performing such an experiment for a materialist is to keep from begging the question philosophically?

It depends on what qualifies as an empirical claim. If an empirical claim is a claim that can be only seen through science, then no. Since we cannot scientifically prove or disprove the historicity of Jesus short of a working time machine. If an empirical claim can be tested via written accounts and deductions from what we know about history, then yes.

At risk of derailing the conversation towards the historicity of Jesus (a conversation which I hope you indulge me we not go into since I feel I am not well-prepared to engage in it), should there be empirical evidence that absolutely refutes any of the sources we have on His historicity, then Christianity as we know it (emphasis on as we know it) is false, and the intellectually honest thing to do is to stop asserting His historicity as truth (emphasis on what is being asserted).

Um, your assumptions seem to be showing.

But the existence of Jesus is an empirical claim, is it not? He really existed, right?

I don't believe that the Bible answers any empirical inquiries. The Bible in a nutshell says that God created Heaven and Earth, and that through His Son, we are saved. It doesn't tell us how and why. That's where science comes in. I hope that makes sense.

I've thought about it, but i can get too wordy and sidetracked. Others here would probably do a better job...