Christianity is fully compatible with a society where people can make meaningful decisions over things which affect them, with democratic control their workplace and community. In fact Tolstoy came to this conclusion, that Christian ideology says we should have no bosses, and not dominate or control other people.
I suppose there are various right-wing ideologies, and some of them may be compatible with Christianity. I cannot imagine any left-wing ideology (which is at best wrong and at worst downright evil) compatible with Christianity.