The military itself has an annual budget that's approved every year. A govt shutdown doesn't cut off our access to that money; it's already been made available at the beginning of the fiscal year. A shutdown just prevents the govt from approving the next year's budget.

But the shutdown does affect service members' individual pay, since that's handed out twice a month (on the 1st and 15th). And it's not like we can just not work until we get paid. The way our contracts work, we're essentially on duty 24/7/365, for as many years as we signed up for (usually 4-6 at a time). We're authorized "regular leave" daily so we can go home, eat, sleep, and recharge for the next day. Because of that arrangement, we're always on call, expected to work whatever shift we're ordered to, and go wherever in the world the military needs us at a moment's notice. And it's impossible to work overtime if you're always on shift. Unless they enact "stop-loss," which prevents us from leaving the service when our contract expires. The Army did that for the Iraq War; a buddy of mine was stuck in the Army for 17 months past the end of his enlistment contract.

Especially since every shutdown has been from the party of “support our troops”.

If there's anything I've learned in the 20 years I served, it's that Republican politicians use the "support our troops" line to win votes. But in reality, they don't give a shit about service members or veterans, and have regularly been voting to defund programs that actively help and support us. Democrats have done more to help military members, veterans, and their families, than Republicans. Trump himself didn't want anything to do with us unless it boosted his image with his constituents. I believe he called our MIA/KIA/POWs "losers." When I retired last year, almost every military member I worked with was voting Democrat. Fuck the Republican Party.