Well, 1st off, it won't hurt ONLY the independent dealers, it'll also hurt BP, which is the whole point of the boycott. And 2nd, if they're truly independent, they could switch to a different supplier.
But, the apologists come back, they're not THAT independent. BP has tied them down to long-term contracts. I've likened this to the Taliban holing up in elementary schools, which is despicable conduct, to be sure, but effective, since we don't want to blow up school kids just to get the scumbags who've taken refuge among them.
So what CAN we do to hurt BP without damaging the gas stations who peddle their products? I've got 2 answers for this:
(1) Personally tell the station manager to post a huge sign out front saying "My contract with BP runs thru (date), and I pledge to buy my gasoline elsewhere when it's done." If they'll do that, continue to give them your business. If not, go elsewhere.
(2) Stop in and support the merchant by buying convenience-store products — milk, bread, beer, snacks, ice, etc. (which is where they make most of their profits, anyway) — but when they ask "And did you have gas, too?" tell them "No way, not as long as you're selling BP."
You DO have a choice, and where you CHOOSE to spend your money DOES make a difference.