No, I wouldn't. For what it's worth, it's Bloom and Barber's toy and they can do ban who they want, it's just not a precedent I'd be entirely comfortable with.
In fairness, and I if read that particular condition correctly, it applies to anyone who buys or maybe (in my case) is named on tickets as the person attending the match regardless of the team that I support. To suggest that I'm obliged to protect and enhance the BHAFC brand is a little fanciful...