That's one side to it, and it's a fair thing to point out. The other side of it is the association with negative stereotypes. One person's heritage most definitely can be another person's oppression, though. Note, I'm not trying to take sides, simply pointing out that that's not the only view.
Full disclosure: I'm generally against political correctness, and a very strong believer in free speech. If some horrible group wants to gather and say hateful things without causing a riot, they not only have that right, but as a citizen, I also have a responsibility to tolerate it. Shining a light on abhorrent speech is the best disinfectant, as it clearly fails the test of treat others how you want to be treated in a just society. It's also highly preferable to use logic, persuasion and consensus over more volatile methods of handling, especially if it escalates the conflict.
The war chant at games however, does not fall into the 'free speech' category. The university team is a government institution, like it or not. So the next question is where does this fall when it comes to government speech. Honestly, I don't have a great answer, nor have I studied the arguments of those who are against it. Government is usually pragmatic though, and attempts to be responsive while taking the path of least resistance. You can't go to the DMV and get a racist license plate. What is racist? Well, some bureaucrat decides based on who has complained, and how loudly. Honestly, I'm ok with that, as I'm not sure how you come up with a better system.
I don't like the controversy over this stuff, but it's fair game IMHO. I will say this: I'd rather have Illinois sports get ahead of this stuff. New traditions get started all the time, and the best ones usually stick around.
And it's sad to say this, but there's apparently no way for boosters who like these traditions to buy off those who don't. I'm thinking about teams like Florida State, that have the same issue, but have been able to find a mutually acceptable solution by getting tribal support. I mean, if I decided to call you Melvin, and you didn't really care for the name, you might object. But if I did exactly the same thing and offered you $100,000, you might find yourself loving that name. I don't know the details, but it seems both scummy and ingenious to resolve it that way.
Btw, anyone who wants to make fun of my ancestry for large sums of money, feel free to PM me.