Should certain universal truths be taught?

Always. The question that follows, however, is what are universal truths and where should they be taught. If the universal truth is the periodic nature of electron structure in chemical elements, which is a universal truth (and the underlying mechanism by which chemistry works), present it in science class in public school or anywhere it is appropriate. If the universal truth is that there is a God and He is the Creator of all things, then teach that in Church and at home as well as in private school, if desired.