incorrect. Religious institutions are a unique protected class of organizations under the Constitution. Greempeace and their ilk are not.
The only thing that separates churches from other 501(c)(3) organizations like Greenpeace, etc is churches are automatically considered 501(c)(3) & need not apply for that designation.
Otherwise, all 501(c)(3) groups are basically the same. If you think the religion clause of the First Amendment protects churches in this manner, you are wrong. If you think the free speech clause of the First Amendment protects churches in this manner -wrong again.
Precisely because no one is forced to be a 501(c)(3). With the shekels come the shackles.