Of course all fanbases are diverse, but certainly some clubs have certain tendencies and others different ones. You can like it or not, but every situation of an individual fan acting in a certain way helps inform the general perception of a team.
I can speak to the teams in Prague, Sparta has a reputation for having a lot of racists, though as the most popular team in the country they naturally have all kinds of fans, but if you're going to a game are you going to go in the supporter's section? Not if you don't want to be hanging out with hardcore hooligans. Slavia for whatever reason has a bit more of a neutral reputation and lots of people who consider themselves intellectuals prefer it, but at the end of the day they have a huge contingent of neo-Nazis, in my view they are just as racist as Sparta, but they are not viewed the same, and it's largely because of high-profile things that Sparta fans have done, the trouble they've got in. It is also the fact that when Slavia fans do racist things, the club condemns it more convincingly, whereas with Sparta you can tell the club whatever it says is actually weaker than its hardcore fans.
My local side Bohemians is the only club in the Czech Republic to largely profile as all-around tolerant and anti-racist but we also have racist fans, and in fact great numbers of fans who actually take offence at the club being painted as "leftist", appealing to "leaving politics out of football". They are bothered by the club's anti-racist profile the same way anti-racist fans are bothered by racism in the ranks of their respective fanbase.
So of course all fanbases have all kinds of people, but what is naive is thinking they don't also have a profile, as unfair as it can seem to the many people who don't agree with it.