I'm going to use the term "audience" here partly because it's convenient, and partly to push your thinking. If my use of that term predisposes someone to judge me, well, I'll try to survive.
Performance anxiety can happen if
- the band looks too "out there" or "too staid";
- the music is "too secular sounding" or "too churchy sounding";
- the music is "too loud", "too quiet", "too new", "too old", etc.;
- "they shouldn't use those instruments";
- the stage, light show, etc. are "too showy" or "too much like a rock concert".
In short, if we're busy judging the band by their performance, it's we who have the performance mentality, not them.
So... for everyone in the pews, chairs, aisles, and so forth... how's that working for you?
(Dear worship band, the same thing applies to how you look at those not on stage. Don't judge by external reactions. Don't demand people sit still, dance, or anything else. Let God deal with each one.)