That reads like a clause out of a contract of employment and if it were I'd understand it's validity. But as a customer it's not my job or responsibility to uphold the good name of a business ( and BHA is a business ) just because I buy their product. I shop at Aldi, I despise their parking...
While I realise the club have the right to stop anyone they like going to a match for any reason, or even no reason, and I can guess as to the subject matter of the comments, since when has it been a football clubs job to police social media of private individuals ?