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
There are many churches that are very politically active, preach politics on Sunday and pay for political advertising.  

Pulpit Freedom Sunday was an annual event where conservative pastors filmed themselves endorsing candidates, telling their members which candidates God wanted them to vote for or against and preaching political sermons, for the stated reason that they wanted the IRS to attempt to revoke their 501(c)(3) status so they could fight the case to the supreme court to get their political restrictions under the law removed.

The IRS failed to respond to any of their activities.

Churches are already political stakeholders.