Boozhoo!
In cases like this, I personally think it's appropriate to reiterate that they are welcome, but to politely and firmly establish that these drums are actually consecrated in very specific ways to certain traditional purposes, and that out of respect for those responsibilities you have to ask that they only perform songs in ways that are consistent with those traditions. For example, you could say "there's absolutely nothing wrong with those other beliefs you have, but they should be reserved for their own setting too. This drum is only meant to make songs that are traditional to our tribe, and the new-age astrology, chakra, crystal stuff is considered an intrusive element to those traditions."
I've found that some new-agers are actually surprised to learn that their ways are intrusive, since they've been brainwashed to think that Indian spiritual actually IS all about energy vortexes, crystals, astral stuff, etc. When they are finally told otherwise, it might even be a moment of liberation from some of those delusions.
But to stress the point, those drums are sacred items. In the hierarchy of important things, it actually matters more to protect them, spiritually, than to just be polite for politeness' sake. Being welcoming is a worthy virtue, but it comes beneath being a steward of the things your grandparents gave their lives to protect for you. So in context, I hope that helps address the conflicted feelings you might have.