system
A chat on subreddit /r/NoStupidQuestions
human
The Catholic church has a large lobbying wing. The Salvation Army lobbied Bush Jr. directly.
gpt
Currently, their lobbying wing is separately financed, with a paper-trail to back it.  That would all go out the window, or get more complicated.

Lobbies are tax exempt.  Charities are tax exempt.  Nothing would stop big Churches from becoming those very things.

It's one thing to take away the Church exemption directly, another to say "you can not be exempt if you are not secular regardless of any other factors".  Even people weak on "freedom of religion" would have to perk up if the Salvation Army cannot be exempt but a Far Right anti-union or anti-immigrant lobby still is.