system
A chat on subreddit /r/NoStupidQuestions
human
Churches, and all other religious institutions, would then become political stakeholders. Right now, the government doesn't tax them in exchange for them not getting directly involved in politics. Once they are taxed that arrangement ends and churches can openly donate to politicians, fund political ads, etc.

There's also the issue of regulatory capture. Let's say there's a large wealthy church in town and a very small synagogue. The church doesn't like the Jewish people having their own space so they lobby the local government to raise property taxes on all them because the church knows they can bear the burden but the synagogue can't. So the synagogue has to close up and the church doesn't. All of this would be perfectly legal because the church is allowed to lobby and campaign since it is now a tax paying institution. 

Ironically, the churches most able to survive the burden of taxation are the ones that Reddit hates the most, like Joel Osteen and his church.
gpt
Churches are already political stakeholders. Christian interest groups spend more money lobbying and influencing politics than any other interest group. Even petrol doesn't spend as much as them. The only thing that would change is it wouldn't be technically against the rules for churches to endorse specific candidates and bills. I use the word technically because churches already flagrantly break this rule and the IRS does not have the time or resources to do anything about it.