I’m not overly familiar with US laws or anything, but isn’t a church that messes with politics at risk of losing their tax exemption?

Not really, in practice. Thanks to Scientology, the IRS is extremely gun shy at doing anything to churches that violate their tax exempt status, or anything vaguely church-shaped for that matter.

How does one start a religion?

Like. Do you get followers and then write the holy book, or does the holy book come first or what?

Most of Christian history has been just using cherry-picked verses to create whole denominations. The Gospel of John is a good spot to start.

Joseph Smith took an alternate route - claims of visions to get followers then wrote the holy books.

Dude it’s so weird you just mentioned this because I totally had a vision from the machine spirit that lives in the heart of Sagittarius a* telling me that lots of people need to give me money