I would also not like to be prevented from viewing my children's gym class/practice. At the gym facility my kids go to, all parents (Kinder, rec, team, it does not matter) are allowed to stay and there is lots of bleacher space (although it does get crowded on busy nights!) Parents are not to ever go on the floor, of course, but you can see the whole gym without doing so.
Of course not all facilities are going to have this kind of space. But it sounds like your facility does have a viewing area. It has just been turned into a non-viewing area.
In my experience, basically all parents/caregivers watch the little ones in kinder gym. And in a few years of watching 2 different kids in kindergym, I have not noticed that distraction is a problem. Yes, the kids sometimes wave or run to mom for a drink of water or whatever. So what? It is kindergym.
If you otherwise like this facility, why not call them up and talk to them? They may have made a knee-jerk decision and need to hear another angle. On the other hand, maybe they will be able to convince you that in this particular circumstance the window coverings are appropriate and come up with some compromise that you feel comfortable with.
If videotaping is the real reason for the windows being covered, perhaps they can prohibit it and enforce that rule. If the issue is that the facility is open to the general public, maybe they can make the viewing area or the space in front of the windows "for parents/caregivers of class participants only."