I don't feel that someone whose act involves taking some of their clothes off is automatically any more objectified than someone who comes on after them & sings, though.
I daresay I objectified A-ha quite a bit, 25 years ago.
Look, I'm not a huge fan - I do seem to have seen a fair bit of it recently, though, on the same bills as my dh's band, & some of it I enjoyed. Some of it I think is rather cleverly done (there's a lass called Twiggy Starlust who does a good parody of androgynous male glam types...) - but I'd not pay to get into an evening's worth of it.
Is any sort of onstage nudity objectifying? Burlesque aside, the last time I saw any was a revival of the 'Romans in Britain'.