[PeterisP]

From the employer's perspective, the definition of "extreme political views" would be the labor rights / pro-union parties (wherever there's not a two-party first-past-the-post system like USA, those often are explicit separate parties) and the communist party, but the working class would very much want that employers don't get to make that decision.

The criteria for too extreme should not be specific to employment. If some organization is considered too bad to exist (e.g. the Nazi party in post-WW2 germany), then it should be dismantled as such, but if the country considers a political movement legitimate enough to participate in elections and gain seats in government, then obviously supporting that organization or membership in it shouldn't be an obstacle for employment as well. I have no idea on what the legal status (if any) of KKK is today in USA, but whatever it is, IMHO it should be the same both for politics and employment.