The invasion of Iraq predated the current level of interest in the name of the Washington football team, although there were BS issues the media wasted their time on during the late 90s and early 2000s, and that time would have been better spent on Middle Eastern politics.
I haven't seen much indication that there's a problem of Native Americans being called redskins by white strangers.
I think cultural appropriation is normal, and usually okay, with a few extreme exceptions (blackface.) Much of the left-wing pushback on it has been absurd, like the activists pushing the UN to make it illegal, or protests of a painting of Emmett Till's open casket funeral because the artist was white.
https://i-d.vice.com/en_us/article/y...iation-illegal
https://www.nytimes.com/2017/03/21/a...-protests.html
The mainstream media also treats organizations like the Times and the Post with more respect than Fox News.
I'm not a fan of Fox News, but it largely exists because the mainstream media had a partisan bent in the other direction. There is explicitly left-wing journalism (The Nation, The Daily Kos, Mother Jones) but those organizations are open about their leanings, whereas much of the press pretends to be non-partisam.
Tom Cotton's op-ed didn't call for war crimes. He was calling for the military to perform the same role it did against anti-integration protesters in the 60s. There is an argument that people with military training will be readier to handle riots safely than the average police force.