Here's an interesting question: The NLRB says you can't fire someone for union organizing, but does it say you can't refuse to hire someone for union organizing?
Yes. A friend of mine in college (who had the highest LSAT score of anyone I knew, and went on to become a lawyer) joked that his strategy would be to announce during an interview that he planned to organize, and if he didn't get the job that he would sue them on the grounds that they rejected him for this.
Right, but that's on the same grounds as refusing to hire someone because they're black/Muslim/some other minority of some sorts. Becomes very hard to prove.