First, take a deep breath caracatita, and relax a bit.
Some people choose to believe only in what they see with their own eyes, but then they learn that their eyes might deceive them (see for example this post in a discussion on faith). Some then turn to "measurement." Of course not everything which was considered proven with a lot of proof behind it turned out to be true. Alas, we now know that everything you think you know and are taught in biology classes for sure is going to be proven false at a later date. And yet we survive and we go on with it. In fact you are taught many things which we currently actually know are false (e.g. Newtonian mechanics), and yet they are comfortable to lean on for different reasons.

"I am taught to demand proof, and I am taught that if there is no evidence to back a thing up to act as if it does not exist."
What do you actually know for sure? Evidence is a tricky word. In courts they often use the term 'beyond a reasonable doubt' but that's subject to much interpretation.

Notice your daily activity. Do you really believe only what you have clear evidence for? For example, a very classical example, you think you know that if you drop a cup made of glass on cement, from 2 meters high, then it will break. How do you know that? Already Hume showed that you have no clear evidence for that yet you believe it on the basis of an unbased belief in induction.
Another example, you believe what your teachers teach you, with very little evidence for it. There were attempts at the beginning of the century to completely prove mathematical proofs, but alas it is pretty much impossible for anything more than the most basic proofs, and all mathematical proofs you currently completely trust are only considered true because a certain group believes them to be true. It's a very serious group, but nevertheless every once in a while even an accepted mathematical theorem turns out to be false. Oh well, that's life.

Or, for example, you said: "pseudoscientific New-Agey postmodernist drivel" You use those words, but do you actually know what they mean? I doubt regarding at least the third word, and yet you use it, like we all constantly use words we don't understand. This is how we use tools in the world. We have a somewhat vague idea, an intuition about them, and we use them. Sometimes we're right sometimes we're not.

So yes, we discuss here what we believe. We discuss our thoughts and opinions. People read them, and then they can take it or leave it. Similarly to your teachers - some professors you should trust, others less so. Some are based in reality, others less so.
As Edna Stern in post quoted Seneca saying: “Whatever is true is my property”  and everything else you can either throw away, or better, try to learn from people's erroneous opinions.
We are all here because we believe that someone's else opinion can actually teach us - even in the case we disagree with it.