Personally, I think it is a poor and unwise business decision for a gym owner. Although I would not be "outraged" ( assuming the parents of the kids in the video signed some kind of agreement), as it is technically the right of the owner, I would find it uncomfortable to be part of the gym if an owner was using the gym as a political vehicle.
Where I live, in a major US city, I regularly socialize and do business with people with quite extreme political views (on both ends). If an ad got out that our gym owner supports Candidate X, especially if she/he uses the gym or athletes in promotions, that pretty much seals the community impression that "Gym is Republican" or "Gym is Democrat" or even “Gym is Fundamentalist Christian”, or "Gym is Socialist”, “Gym is Anti-Israel”, “Gym is Homophobic”, "Gym is pro-life/choice".. etc, etc, depending on the platform of the Candidate in question. People are quick to associate labels with any information about a person or business’s known affiliations.
As a parent, if I then mention that my children attend this Gym, it might be assumed that we support this Affiliation & Candidate. Potential new customers may wonder if their child will fit into a “Republican” gym, etc., or outright refuse to associate. I might find myself in conversations like "Sure, Owner is a strong Socialist Democrat, but there are plenty of moderate and right-leaning families, too, and politics don't really get in the way of our gymnastics - I don't think your child would be discriminated against..blah blah argh I hate this conversation....."