Timing is everything. These songs which you say get the audience groaning are usually ones they know well and early in a performance they want to listen rather than join in. However, later in the performance, especially if it is in a pub, having loosened up they will join in with gusto and enthusiasm the self same songs.

Read your audience. Judge their disposition and choose your songs accordingly. Rather than performing a set programme, ask for requests and if one such song is requested and gets the 'groan' from the rest of the audience, decline to sing it, but if there seems to be a call for it, sing it and encourage the audience to join in with you.