I'm headed to Zion next Wednesday....
Red Rocks is BLM land that will definitely close as well. A good part of climbing around Moab is federal land too. If everything does get shut down it will be curious to see how it's enforced. Whether it be soft in that you can still walk in or hard in that it gets you arrested.
I'd think that in Zion you could still climb on The Watchman, the Three Marys or West Temple unmolested as they sit on the perifery of the park and are approached from town. Supposedly the road through the tunnel would be kept open which is where a lot of cragging is found. Though I could see them enforcing a closure there by not allowing any parking.
Lots of sport climbing around St George as well including a sort of mini-"Red Rocks" at Snow Creek Canyon State Park that might entertain for a day or two. Best of luck.