They have the same rights to refuse tatoo parlors as you do to open one, if not more so since they occupy the majority of the community. Personally, I dont want tattoo/piercing parlors, porn or head shops, crack houses or more liquor stores in my neighborhood either and actively petition to keep them zoned out. Dont care what others think as long as they keep to themselves and dont try to force their ideas on others.
"It seems to me the biggest bigots are actually the ones that insist you MUST accept their ideas or say things a particular way and you're bad/racist/sexist/prejudice if you don't".
It's their community and since they arent hurting anyone they have the right to tatoo parlors out. Tolerance goes both ways.