The basic question:
What if a polite request is met with rudeness?

My suggestion would be to POLITELY escalate.

1. You stop playing.
2. In a voice loud enough to be heard by the entire crowd (don't shout) you look at them directly and say politely but firmly, "Will you please stop playing your bodhran and your shaker while I am performing."
3. Continue to look at them directly until you get a reply.
4. If they refuse your clear, polite, direct request, you stop and make it clear to the assembled multitudes that you have stopped and will not resume. Be polite.
5. If they agree, in a voice loud enough to be heard by the entire crowd you say, "Thank you" and resume.