How important are cutting-edge technologies for one's career?

I saw this comment on workspace stackexchange:

I think you are underestimating how much working on legacy stuff can set a developers career back. From the point of view of getting your next job it's basically a gap in your resume at best.

This was controversial, so let's discuss...

Probably, if you want to work on cutting-edge technologies in your next jobs, you should be doing it now. But let's say you mostly care about money (or status or groupies), does it matter if you do Cobol, Java or React?

Do people often totally switch to different stacks in their career?