Costin Moroianu said:
The "don't get involved in politics" stuff seems more like enlightened self-interest, self-preservation, or simple common sense. When Witchers were new, they wouldn't have wanted to be entangled in politics becuase that would result in them being used as a military force rather than as monster slayers, which kind of defeats the point of having them around. By Geralt's time, Witchers are hated and feared, so getting involved in politics would give people even more reason to want to hurt or kill them.
Vesemir does try to drill the recruits on this, but Geralt was a bit of an idealist, seeing himself as a hero; for instance, he went to save a young lady from being raped, but she made it pretty clear she'd have preferred that to being anywhere near a Witcher. Getting involved in anything not directly related to monster problems usually doesn't turn out too well for Witchers.
Geralt gets tied up in politics for the first game because he wants Salamandra and the only way to get to them is via the Temerian court. In the second game he's busily trying to extricate himself from the court and all too soon needs to clear his name after being falsely labelled a regicide, but these are unusual circumstances to say the least.