It depends on how you interpret the title of the thread - is "shouldn't" prescriptive or advisory?

I think there are very few songs that must not be sung in a UK folk club. I think it would be very unusual for singers to be prevented from singing a particular song, unless it was especially provocative. However, there are plenty of songs which may not receive the reception the singer might have hoped for. In that sense there are many categories of songs which a singer should at least think carefully about before presenting at a folk club.

Political songs are one such category. If you're going to sing them, then you should be aware that not everyone in the audience may share your point of view. I recall a fairly recent thread in which some people appeared to be genuinely surprised that not all folkies are dyed-in-the-wool lefties. Some topics, in some areas, are particularly sensitive - Dick has already described the situation in Northern Ireland, and if you choose to sing an Irish rebel song in Aldershot or Colchester then you should be prepared for a strong reaction.

Rugby songs, while possibly one of the few remaining examples of genuine folk song, would probably not be acceptable in a folk club, for different reasons.

It is up to the singer to judge their audience - which they should do as a matter of course, whatever they sing. If they choose to sing something which may be provocative, then they should not be surprised if they receive a hostile reception.