I wish basic logic was taught starting in junior high school. Ideas such as truth tables and valid rules of inference should be common knowledge. Not so long ago, geometry was once the linchpin to later studies of logic, but that, sadly, no longer seems to be the case. An exposure to the notion of mathematical proof and some of the standard logical errors should be much more common than it is. Even if the math is never used again, the precision of thought is invaluable training.
In regards to religion, I have seen some absolutely silly arguments made about the impossibility of infinite regresses that some basic set theory would shed light upon. Other notions, such as partial orders and equivalence relations would, I believe, help philosophers immensely if they would just take a bit of time to learn them. If nothing else, it would fix some very poor arguments about 'greatest' things necessarily existing, etc.
Maybe too much for many, basic logic would be something though but some religions forbid even saying their gods name let alone question it.