The reason I would not sing a song at the same venue where someone else sings it regularly, is that life would become exceedingly boring.
If that song was sung every week by various people no one would eventually want to sing it ..... definitely overkill.

There are far too many good songs around for you to have to double up and sing one that someone else has undoubtably taken a lot of time and trouble to learn.

I pride myself on singing songs that are different and that folk club regulars would not normally hear.
If, as does happen, someone else expresses an interest in the song ...I will leave the song alone and move on.