I don't think it changes their mind, but it does let them know that I see their beliefs for what they are. A lot of the most bigoted beliefs are protected from self-scrutiny beneath a mantle of divine sanction informed by the person's religion. They actually think their belief is good and moral. I do think it's worthwhile to staight up call that out for what it is, -pure and simple run of the mill bigotry. When you're holding bigotry up on a pedestal as a belief system to aspire to and admire, you need to know that the rest of the world not only doesn't agree, but sees it as actually immoral and damaging. Polite deference isn't always enough.

But again, I basically never call someone with bigoted beliefs a bigot to their face as it isn't generally productive on a face-to-face basis. An exception was my dad, who, when faced with my opposition to his thinking homosexuality was wrong and gays be allowed to marry, asked me if he was then a bigot and demanded I answer him. I had to inform him that sadly, yes, he was, but I still loved him and he had a lot of other great qualities :) He found out later that year that his daughter was gay, and now he magically changed his stance :P Funny how that works.

It's also important to keep in mind that calling someone a bigot if they actually hold bigoted beliefs isn't a slur or an insult. It's just a truth they hate hearing and it's considered a truth that is impolite to speak out loud.