Maybe it would, people can sue fr any reason. Unfortunately the burden of proof is on them. It would be more difficult if the worker was under contract, but most are at will employees, meaning they can be fired for any reason, or no reason at all.
The DNC wouldn’t be required to hire a republican, and could fire them if it was later found out. If you are an avowed enemy of the company you work for by way of voting for this marxist, you should be fired. No question about it.
Any leagal reason that is. You cannot be fired for race, religion or age. But that’s about it.