The Washington team is a straight up slur, which is the principle issue. On top of that, the team has long been adamant that they have no intention of changing the name, drawing further ire. Nike has pulled all apperal from sale, meaning that any company that has a contract to sell Nike merchanidse can be found in breach of contract and may no longer be able to sell any Nike gear. Since Nike has exclusive rights to NFL merchandise, if they don't want to sell it anymore, then no one gets to buy it.
The Blackhawks are named after 86th infantry division, which was in turn named after Blawk Hawk, a Sauk war chief. Native groups are nearly unanimously opposed to the logo, but seem to be split on the name itself.
The Chiefs are named after KC Mayor Harold Roe Bartle, whose nickname was "Chief". The Chiefs have only been asked by Native groups to address offensive behavior such as headresses and the tomahawk chop, and not the name.
The Braves has a basis in Native sterotypes, but they have moved towards a much more generic interpretation of the name in the past few years, such as tweaks to the logos and changing the mascot from Chief Noc-a-Homer, to Homer the Brave, to Blooper, who has zero connection to any Native imagery at all. They are currently working with the Cherokee and Muscogee Nations to alter any team traditions that may be viewed as offensive to natives, and likely won't be bring back the chop next season.
As per Notre Dame, it was founded as a Catholic instiution. There is some debate on the origin of the moniker, but it likely comes from the large body of Irish students that were found at the nations premier Catholic University, which is to be expected. This is similar to how Canadians have no problems with the Vancouver hockey team being called the Canuks, but would likely have some problems with an American team using the name.
And if you stop being a fan because they change the name, then I really question your actual commitment to the team. Team names and logos don't win games, the players and coaches do. Dan Snyder's horrendous ownership descisions are a much better reason to not want to be a fan anymore.
I don't like McDonalds, but I'll take all your Big Macs