I like the interpretation of Hans-Hermann Hoppe about it, in the book Demokratie der Gott der keiner ist. Basically the Catholic church despite many abuses along the centuries was a break to political power centralisation and defended private property and individual rights, like in mediaeval times, but every now and then it gets infected with terrible wrong ideas and destroys the good ideas of the past, like the time we're living. One must always use reason, and don't take things literally from the bible.
Discussion
I think unfortunately, if the church had stayed faithful only to the good ideas of the past (commandments, life, liberty, property, etc.), it would have disappeared very quickly because these are very idealistic principles by nature that can be easily corrupted by bad and greedy people (the absolute majority of people). In a way, the infection with terribly wrong ideas was a necessary adaption to reality, which was very effective as we are still discussing this 2k years down the road.
Also regarding the role of the church as a symmetry breaker in the political system if the medieval: It could be true for later times, but in many cases the church was the origin of this centralization and, hence, the power. The Vikings (and later also the Normans) adopted Christianity to strengthen their power, for example, in Kievan Rus‘ and Normandy.
Thanks for mentioning the book. I will take a look at it.