People have done social experiments about white people lawfully open carrying and minorities lawfully open carrying. Police got called much more on the minorities. Though these were not rigorous scientific studies, so to be taken with a grain of salt.

Biased is more like it. And funny enough I personally haven't seen any activists against guns here in Ohio so far(though there probably are some).

Racism against gun owners isn't a real thing. Bias maybe is what you're looking for.

i think the word you mean is bigotry
gun owners are of many "races"