You are right, there is a pattern of Fascists coopting the church to gain power (historically, usually Catholics?) Here is my take:
https://scottvern.medium.com/oh-no-the-catholics-are-coming-again-678aa0038c93
As stated, I believe the best modern example was Franco's Spain in the 30s. He railed against Socialists and got the Catholics to hate on their "bad morals". Later, the Catholics learned that they had been duped, as Franco created a dictatorship largely without them.
Conservative churches will soon have a reckoning with their core value systems...I mean, how can a church stand for intolerance? (specifically racism, violence, and homophobia?)
Thanks for warning us...this evil phenomenon cannot be profiled often enough!