I haven't really been paying attention to much in the way of this shutdown but this just another reason why it pays to do some of your own forecasting!
The notion that anyone is doing their own forecasts in this context is a bit misguided. Consider the following...
If you use any operational NWP models you are subjected to the whims of government as well. The NAM, GFS, RAP, HRRR, and all ensembles and flavors therein...all federal government sponsored products, and all subject to go down in the event of a long-lasting total government shutdown.
Also, balloon soundings to depict upper-air conditions? Launched by NWS offices (federal government).
METARs? A large fraction are owned or operated by the FAA (federal government).
Satellite? NASA
Radar? NWS
We long ago entered a realm in which no single human being can really forecast beyond a few hours (say 6-12) skillfully without the use of some sort of government-sponsored technology.
And no human can outforecast any modern NWP model beyond a day or so. That capability ended at least 10 years ago.
Yes, there are a handful of private/non-federal entities that provide other products useful in forecasting. If you're plugged into one of them (e.g., WSI or Vaisala), or you're paying for non-American weather forecasts, then you still have a resource. Many universities also run their own weather models, but consider that all of the big schools (TTU, OU, KU, CU, CSU, PSU, UWisc, UWash etc.) get a ton of research and computing funding from NSF...also a federal program.