I'm not so sure. The study discusses specifically people who engage in partisan subreddits, which is not the same as being politically engaged. It also uses an AI to grade toxicity, which surely mischaracterizes many interactions.
For example, I have been in communities of a non-political nature, where political discussions occur. These are often about real issues that affect real people in the community, and yet there are people complaining about political content.
To complain about political content is, at best, a very privileged take, demonstrating that you are in a position where politics do not affect you much. At worst, it is actively hostile behavior with the goal of continuing the status quo and shutting down discourse. I would call most of these kinds of comments "toxic", and yet the rhetoric is usually fine, so I doubt an AI would agree.
Do you have a source that sports are a net financial positive for schools?
Here's an article about students being charged thousands of dollars each per year for sports programs: https://www.nbcnews.com/news/education/hidden-figures-college-students-may-be-paying-thousands-athletic-fees-n1145171
Here's an article showing that only 25/65 Division I schools had a net positive revenue from sports: https://www.bestcolleges.com/news/analysis/2020/11/20/do-college-sports-make-money/, with those losing money losing a lot more than the ones making money.
Another: https://www.pbs.org/newshour/economy/analysis-who-is-winning-in-the-high-revenue-world-of-college-sports
Just search for "college sports net revenue" and I'd be surprised if you find much, if anything, that agrees with you.