Protestants, at least, have the idea of the "priesthood of all believers", meaning roughly that each person can have authority in doctrinal matters. So you should listen to your priest, but you don't have to accept that he's correct if God is telling you something different. Thus the billion different protestant denominations.
Protestants if you go back to their roots actually expected you to become an expert in scripture in order to recognize when your "priest" is wrong. But they didn't promote anything goes. It's more that you should learn and be able to apply scripture correctly. This didn't prevent the proliferation of denominations because of course different people would interpret a piece of scripture differently and get really worked up about it.
This is in contrast with Catholicism, where pretty much everything was conducted in Latin rather than local languages; the emphasis on layperson understanding of theology was a direct response to the trend of most followers having zero understanding or ability to understand the scriptures and sermons they were expected to follow.
Of course, this also resulted in the more decentralized power structure relative to Catholicism's. Quite a bit of Protestant philosophy and tendency stems from immediate responses to a perceived-to-be corrupt and exclusive Catholic Church.
