The withdrawal of federal funds for any institution not abiding by the principles of the constitution and especially for any educational ones refusing to even abide by a basic commitment to objective scholarship, would be the quickest and most effective way to solve the problem.
Obama would have pussy-footed around the peripheries of the problem, afraid to do anything that might offend anyone. Trump likes to see himself as a man of robust action. Well he could demonstrate that by fixing the education system in one fell swoop.
All he would have to do would be deny funding to a few of the chief offenders and sit back while the rest of them scramble to clean up their acts.
I don’t know much concerning your comments about the Church. But you are right bout my take. If he is allowing any kind of Church influence in stte policy then I do not approve. I assume Trump is shoring up his support base by appealing to the church. Maybe he got that idea from Putin too!