For the same reason is not ok for a public business to not make cakes for gay couples, we should not allow public businesses to pick and choose who is allowed to be part of the economy. If you want to argue against that, that is fine, but you have to accept it when people with the completely opposite set of morals start discriminating against _you_
edit: In case it wasn't clear, I am not a fan of Nazis, but I don't want to even set up the opportunity for businesses to have the power to just exclude me from normal day to day activity just because the CEO has decided he doesn't like whatever group I am in