I agree with Keef

It's a truly great song, but they have been playing it for 50 years.  At some point it's time to stop and I'm not even sure the reason is important.  Artists evolve and the real fans evolve with them.  They've never done "Jig-Saw Puzzle" in concert, maybe it's time?

Regarding what the song is actually about, here is what its writer, Mick Jagger, said:

In the Rolling Stone interview (14 December 1995, RS 723) Jagger spoke at length about the song, its inspiration and success, and taking credit for writing the lyrics. Keith Richards also credits Jagger with the song in his autobiography.[14] Jagger attributed the success of the song to a "good groove". After noting that the lyrics could mean so many lewd subjects,[15] he again noted that the combination of those subjects, the lyrical ambiguity was partially why the song was considered successful. He noted, "That makes it... the whole mess thrown in. God knows what I'm on about on that song. It's such a mishmash. All the nasty subjects in one go... I never would write that song now." When interviewer Jann Wenner asked him why, Jagger replied, "I would probably censor myself. I'd think, 'Oh God, I can't. I've got to stop. I can't just write raw like that.'"[16]

I don't understand some peoples' need to rewrite history.  The reason the US now has laws banning discrimination based upon race is because historically the US was a systematically racist society.  Prime examples would be the race based slave economy or the Indian removal policies.  Sadly, vestiges of the systematic racism still exist today.

The Rolling Stones like to court controversy in their lyrics and they are not above making direct social commentary.  But what would your reaction be if the Glimmer Twins wrote a song about the concentration camp guards enjoying some "Jew Sugar" in the joy divisions?  It's only rock 'n' roll, right!