...Belong in the "science" category, as "the science of truth", just as physics is the science of energy, chemistry of matter, biology of organisms and so on?

Yes and no. Yes in the sense that it is (or should be) the identification of reality. No in the sense that it is more fundamental than science; it comes before science.

Science is distinct from philosophy in that it requires specialized knowledge, whereas philosophy concerns information available to everyone. But it is totally reliant on philosophy. In fact, the sciences such as physics, chemistry, etc are often referred to as "the specialized sciences." Specialized from what? Philosophy, the basic science.

So it's not that philosophy belongs in the "science" category; it's that science belongs in the "philosophy" category. (as a sub-category, that is)

I've thought about this some more. Yes, I think it makes sense now that philosophy would come before science. The reason I posted this was just a thought about how many people in schools (teachers and others) and academia fundamentally separate science from philosophy.

That is, science as in objective and philosophy as subjective, as their own philosophy would have them believe whether consciously or subconsciously. They percieve maths, chemistry etc. as objective but philosophy as mere opinion or belief, or as I think most students view it: the "other" category of "stuff".

Perhaps this is one of the reasons many school kids don't treat philosophy as important? Because it's written off as nebulous, less serious, incapable of being grasped and ultimately unimportant and archaic?

Yes, because they mis-identify the modern garbage as being the sole holders of the title "philosophy." Because they never see any kind other than the insane kind, they think all philosophy is subjective gobeltygook and thus put it in the dark corner away from legitimate things like science. But this attitude is actually the fallacy of the frozen abstraction.

Yes, that is precisely correct. You have nailed it on the head.

Which is why in the current cultural climate the religious are likely to win out. Since they, like most people dismiss philosophy as pedantic subjectivism unworthy of serious consideration, they look for moral guidance to a church. Where it is claimed that God is the only source of absolute principles, and of course they don't get any argument from modern philosophy on that point.

The mind needs absolutes like the body needs food and water, and people will tend to gravitate towards something that provides for that need, that is people who have any interest in living.

And bingo was his name-o.