Consumers have every right not to do business with someone for any reason they please.

Generally where things go into lawsuit territory is when a business refuses to provide service to someone based on something that has protected status.

In this case, it's likely that Nazis would be labeled a terrorist organization, or a wartime enemy, and would be subject to federally-enforced economic sanctions. It actually would be illegal for Google to do business with Nazis.

I'm not so sure. During WW2, Nazis enjoyed strong political support from the American Right, and the discussion is known as The Great Debate. It was the ambush at Pearl Harbor, and not a clear moral consensus, which closed the debate.

We're talking about Illinois Nazis, not 1945 Nazis. The bums who won their court case - it doesn't seem like the law is stopping them.