Absent the kind of hyper-exaggeration that makes people invoke Godwin's law, no, it doesn't. Your freedom of thought and expression is not imperiled if you get bounced out of a private club for being hateful.
This has nothing to do with Nazis, please get a grip.
Fascism is a clearly defined concept, and there are many examples other than Nazism. In point of fact: it is not necessary to invoke Nazism in order to define fascism.
The kind of autocratic and intolerant behaviour that you suggest is clearly reminiscent of fascism.
Anyway, I have seen the arguments you raise before and I don't really see that we'll arrive at any kind of agreement here.