Yes, it is rationally impossible to be both a conservative and a Christian. Jesus was the original hippie who rebelled against what he saw as a corrupt Jewish religious conservative establishment, sort of what Christian fundamentalism has morphed into today.
But I disagree with the reason that the Catholic establishment didn’t want the flock reading the Bible themselves. The Bible is a mess of contradictions. But the church’s message was that God’s word and the Bible were flawless, so facing contradictions within God’s “holly word” was not something the religious powers wanted the flock to see.