It's very easy to distinguish what makes religion and science incompatible: how they determine truth. Science is empirical, religion is a combination of rationalism and 'received wisdom'. That is to say, with science truth is determined by what can be repeatedly measured, and with religion truth is determined either by rational argument building on chosen axioms, which are generally received from textual sources or from religious leaders.
It is not to say that either one is "correct"; both have their limitations. Empirical truth always has a degree of error, and with anything unmeasurable it is arguable whether it can be assigned a truth value at all -- although I will note that with any truth-finding method, it is a valid philosophy to regard the unprovable as false. Rational truth is independent of our possibly-erroneous senses, it can describe things which cannot be measured (e.g. morality), and things can be true in an absolute, provable sense. Its limitation is that you can make logically true statements which do not correspond to observable reality, especially with badly chosen axioms.
Religion, especially Catholicism, is not empirical. That does not mean that everything it considers true is automatically contradicted by empirical truth, it means that what is true from the standpoint of Catholicism is ultimately decided by faith and not by experiment. There absolutely is a conflict between these philosophies. I'm not going to make a value judgement about any of this; my choice of empiricism does not invalidate or lessen anyone else's choices, although if your choice of truth conflicts with empirical reality you're probably gonna have a bad time. I just wish that the discussion of all of this on Slashdot wasn't so sophomoric: I don't think most peoples' educations has prepared them to have a very elevated discussion on the matter. That as well is not intended to denigrate; I have no college education to speak of and my ignorance is unbounded. I think you make a wonderful, lucid, intelligent, passionate argument, which would be improved by a slightly different conceptual framework. I also agree very much with your motivation; I determined very early on that Catholicism was not for me, but I try very hard to give them their proper respect because we disagree at such a fundamental level, and even if I wanted to disrespect religion, there is never any cause to misrepresent history.
Thank you for writing, as well: whether or not we agree on all matters, I think you do credit to the community here.