I see it as akin to endorsements by various unions (Police, Fire, Teachers, Services Employers, etc), Business coalitions, the Chamber of Commerce, newspapers, NRA, and so forth. If the issues or the expected actions of a candidate affect you, your outlook, or your business it is a civic right for them to express a preference. The Nashville Predators is a sports team but it's also a business tied to Metro government via their lease, taxes, and their location in the city. It's a valid reason to have an opinion--but the Preds "business" and the Preds "my team" are not the same thing and shouldn't have been represented as such.
Gnash shouldn't have been involved. This was Sean Henry as President of the Nashville Predators representing the team/business, and shouldn't have been treated as an endorsement by the players/mascot/broadcasters, etc. That was overstepping bounds but it's also an overreaction to make it about the Preds as opposed to the ownership.
As an out-of-towner, I find this to be puzzling. You don't want your mascot to be in any controversy.
Here in Wisconsin, many teachers unions run their own candidate(s) for the local school boards. In Milwaukee, they have a majority on the School Board and obstruct every Milwaukee School Superintendent who tries to reform anything (which I think is odd, but they get terrific benefits and pay for a system that averages a C- for a grade). The teachers are on both sides of the negotiating table.
The state teachers union also runs their own candidate for the Department of Public Instruction, the people who oversee all school names, mascots (no Indians!) and curriculums. (A few years ago, the DPI threatened to totally defund a public school who had Warriors as their mascot. Nobody bothered to check that it was a Knight in armor instead of an Indian, but that is Madison in a nutshell.) Now the head of DPI is running against the Governor of the last 8 years. The state teachers union doesn't understand why they get flack for their multi million dollar fundraising and endorsements. That seems sort of normal to me, except for the huge amount of money they have, but running your own candidate for governor does seem a little "over the top" as the English say. The Wisconsin police and firefighters don't do any of that.