I think they infested each other. Politicians know they have to get the support of the people so they placate to the religious for votes. Religion sees that it has an ally to help push its beliefs. It becomes a never-ending cycle and we are seeing today how out of control that cycle can get.

Yes and Yes. It's all about keeping control over the money/power. In that way, they are hopelessly intertwined.

The politicians have always tried to use religion to their advantage.
Unfortunately, as is always the case with unintended consequences, the insidious
beast that is religion, infested everything it touched. Just like plague-carrying rat fleas.