I'm going to support them by spending my money elsewhere. you shouldn't fight to spend your money where you aren't wanted or welcome.
What if you were in a situation that was an emergency (urgent situation) and needed to go to the nearest convenient store to make a purchase to address this emergency. The owner denies you service because of your race. You say "fine I will take my business elsewhere!!!" But unfortunately the next store is 15-20 minutes away.
Oh yeah you don't have a car either so walking is your only option.
Should it be fair that business can deny you its service?