Politicization of sports is not a legitimate strategy. Any sort of political influence needs to stay out of sports. Players not only are in sports for the money, but also because they enjoy what they do. Adding politics into the mix could only be detrimental to the sports. If you need proof, look at the World Olympics which have been canceled due to politics or used to try to demonstrate superiority of one country over others.
There is so much money in big time college and professional sports that politics would make little difference. Big spending owners and college presidents have had things their way for so long that politics will not change anything. The game is about money and more money so things will not be changed.
I find that sports are already very much politicized. I think that the NCAA in particular wields way too much power. There are two major problems I have with the NCAA, the first being that future students, coaches and staff are punished for the mistakes of the past with disqualifications from post season, loss of scholarships, etc. The other is that they put rules that are too strict on players for maintaining amateur status while exploiting them and letting schools make money off of them. And I didn't even get into other sports. How about the NHL and the lockout? Another example. The NCAA is the worst offender of politicization but the professional sports aren't far off behind.
There are a lot of cases of players being banned from international competitions because of where they're from. Some of these cases the athlete is indeed from an area that I have some major problems with, but that doesn't mean a person should be locked out of playing tennis. Politics and sports have never mixed well.