Does the paradox of tolerance even exist?

If you tolerate a group that hates a group of people, there are people that hate a group of people, meaning the society is intolerant to that group of people until those people are gone

Exactly: there is no paradox there if you don’t think of tolerance as an absolute. This blog post put it pretty well:

Tolerance is not a moral absolute; it is a peace treaty. Tolerance is a social norm because it allows different people to live side-by-side without being at each other’s throats. It means that we accept that people may be different from us, in their customs, in their behavior, in their dress, in their sex lives, and that if this doesn’t directly affect our lives, it is none of our business. But the model of a peace treaty differs from the model of a moral precept in one simple way: the protection of a peace treaty only extends to those willing to abide by its terms. It is an agreement to live in peace, not an agreement to be peaceful no matter the conduct of others. A peace treaty is not a suicide pact.