Yes, I think that someone is a bigot if that person is biased against bigots, because the people who claim to be tolerant only tolerate themselves. If someone says that they believe different than the tolerant person does, the so-called tolerant person gets confrontational and imposing. The tolerant people need to tolerate everyone, including the bigots.
The term bigotry is usually used as a pejorative toward a really hateful, prejudiced person, but being bigoted is quite simply being too hard-headed and not being accepting of another person or their opinion. So yes, technically you could be bigoted against bigots, and just about anything else for that matter.
I personally think that It has always seemed transparent to me that when people say things like "you are not tolerant of my right to hold (and express) my opinion" (usually involving their superiority over "lefties", blacks, immigrants, whoever) they really aren't making a plea for you to be tolerant, just hoping to trip you up in their pseudo-logic as pertains your "hypocrisy
The simple explanation of a bigot is, someone who doesn't want to understand the views of another person. It's not because you were born a certain way or because you're a racist. People on social media are using the word all wrong.
If we get into an argument of, let's say "religion", and I get angry at you because you don't believe in God and I decide to insult you and call you a "bigot" because you don't want to understand MY VIEWS that there is a God; in turn being a bigot myself, because I don't want to understand YOUR point of views. The word bigot is what I call a boomerang word, the more you use it as a form of insult the more it reflex on you.
So Yes, someone is a bigot if that person is biased against bigots.
I don't really have an answer, I just wanted to say that I think I got a contact high from my keyboard just by answering this question. Like what is a bigot anyway, man? We're all bigots when we're one with the cosmos, man. Far out, man. Far freakin' out.
Being a bigot is not a protected class, nor should it be. Being a bigot implies you are against someone because of the way they were born, for example race or sexual orientation. Being biased against bigots does not make someone a bigot, it just means they do not approve of or intend to let bigotry slide without being challenged.
A bigot is someone who makes generalizations about a group of people and then acts on a hatred of that group of people. To act inhospitably toward such a person is not bigotry, because it does not involve generalization. It is, rather, a reaction to the hatred of a single, particular person. Such an act, by definition, is not bigotry.