Yeah I personally am glad it's on the same feed as it saves me looking several places for Albion news. Plus I don't think it's too overbearing; so far this month there have been only 12 tweets, all of which were focused around the Villa game.
That said, if people don't want to know about it...
For anyone that wants their twitter feed to remain a sausage party:
You can mute any tweets containing the term BHAWFC.
Click SETTINGS - MUTED WORDS - ADD etc.