Supporting one side of a political issue alienates the other side. Imagine if Riot specifically created banners or loading screens that supported an opinion/faction that you didn't agree with. You could simply go about your business and ignore it, but many people would be offended.
You could say, "it's just a game; why would you leave/boycott RP just because Riot has an opinion?"
That argument counters itself— why should a nonpolitical video game be given a political stance? Why would you continue supporting a company if it promoted things you didn't agree with?
Riot can potentially make more money by remaining neutral/apolitical; that's business. Also, I doubt all Rioters stand united with one political opinion for every issue; bringing up politics in the workplace would be asking for trouble (especially with Riot's particular workplace atmosphere). If you were a graphic designer, would you be happy if someone asked you to create a [insert symbol/faction you don't agree with here] banner for the website of the company you work for? You might do it anyway to keep your job, but you'd lose satisfaction with your job and probably become less productive over time.
Before anyone else attacks me for not supporting LGBT (I'd like for you to prove whether I do or don't, or whether or not I might be of that community), I'd like to restate that my idea applies to all prominent political issues. Whether one faction/opinion is right/wrong/better/worse doesn't matter; I don't think it would be a good idea to feature support of either side within the game. If any sort of "support" should be shown in League of Legends, it should be for things that are almost ubiquitously considered "good"— things like when Riot gave a discount for Nurse Akali and used the proceeds to support Japanese earthquake victims.