Breitbart is not the only problem of people who read it, many of them are mentally ill (schizophrenia) or they were raised in a way that makes it almost impossible to discern facts from fiction. Before you argue about that, I can guarantee you that I would - and in fact do - say the same about similar radical left-wing "news sites".
One problem at Wikipedia is that there is generally not enough vetting of the citation sources.
To be fair, that's not entirely their fault, because especially in the US there is a vast network of fake science and news sites powered by lobbyists, and it takes a substantial amount of effort to discern these from reputable sources. I've seen some interesting network analysis of the lobby sites of the US oil industry, and have to say that I wouldn't have been able to easily recognize their think-tanks and science information sites as fake. They're well-disguised and you have to look at interconnections, board members, and funding sources to find out who is really behind them. For example, some of them looked like legitimate sources about green energy technologies, but were in reality designed to poison the climate change debate and further the interests of oil concerns.
Conclusion: Don't focus too much on Breitbart, there are plenty of other seemingly legitimate associations, news sites, institutes and think tanks whose primary purpose is to bullshit people, and they are funded from the left and right.