OK, fair enough.

I would say, apologise for throwing a fit, explain that you have these concerns, hear her out when she explains her side of the story, and let her go to yoga class. It comes down to trust in the end, they’re not going to brainwash her. Even if they do teach a polygamous philosophy, she’s still your girlfriend. Let her tell you about what the classes are like, and how she feels about doing sexual “excercises” with someone (if it came to that!) and so on.

Explain what you want, listen to what she wants, find a reasonable compromise. Again, your initial reaction was probably an over-reaction. Good luck, man.