Okay, history time folks:
The December 2018—January 2019 shutdown was because Donald J. Trump wanted budgeting for his border wall (a higher budget, actually) and refused to sign a budget without it. It was the longest federal shutdown, a fact of which Trump remains proud.
The January 2018 shutdown was the only one (in post Nixon history) attempted by Democrats, to desperately preserve DACA and the DREAM act. They realized shutdowns only hurt the lower and middle classes, and just wasn't a good tactic for the Democrat party. The shutdown ended three days later.
The 2013 shutdown was because Republicans in the Senate, led by Ted Cruz wanted to delay or kill the ACA (Obamacare). It lasted 16 days until the US credit limit was in jeopardy.
The 1995—1996 shutdown(s) came in two parts with Gingrich trying to use balanced-budget arguments to curb Clinton's agenda (while still preserving our high military budget and Republican projects) The shutdown figured both in ending Gingrich's career and getting Clinton reelected in 1996.
In all of these cases, the shutdown failed to work as a coercive measure to get specific agendas passed, rather the delaying coalition causing the shutdown would capitulate once enough misery was had and people were pissed off. Ultimately shutdowns work as a pout holding Americans in (further) precarity as pressure, usually on the gamble they'll blame the other guys.
Right now, the majority of Americans want to see LGBT+ folk have protections against discriminatory practices enshrined into law. The reverse measures are clear fearmongering by the Christian nationalist movement. A shutdown based on anti-LGBT+ measures would easly be framed as neonazi officials holding the budget hostage.
It won't work.
House speaker McCarthy would remind everyone how incompetent he is at politics. He may get ousted with a no-confidence vote.
GOP officials would suffer in elections for the trouble it caused.
The Christian Nationalist movement would be revealed (yet again) it is less interested in elevating the downtrodden than it is in punching down at marginalized Americans. Association with this movement will become a higher risk for candidates seeking office.
I hope McCarthy comes to his senses and takes the signal the Senate just sent to him, and we don't have to go through yet another shutdown.
But if it happens, I expect it'll turn the people further against MAGA and anyone who has anything to do with it.