A business does have the legal right to post signs and say no guns. In Washington state you can still go in, and if they notice they can point to the sign and ask you to leave. If you don’t, then it becomes a trespassing issue. Of course, you also have the right to honor their sign, and not go into the establishment and spend your money there at all!
Are they posting “no firearms?” That is the question. If they don’t post, I can carry concealed all day in there.