It's already illegal for them to do so, it just needs to be enforced. It doesn't even need a massive division.
Have someone look through their social media for political commentary, and send someone to sit in on a random day and see if politics is brought up during a service. Then handle it accordingly. It's pretty straight forward here, either they are discussing politics or they're not. If they are, revoke their tax exemption.
The thing is, they already dare the IRS. The IRS just doesn't go after them. Probably because they'd (churches) turn it into a shitstorm in the media, but I don't know the reality for the lack of motivation.