The Liberals hate these names not only because of the stated reasons, but also because they are uncomfortable with martial values in any form.
They do not want to be reminded that the Sioux were incredibly brave fighters because then they would have to acknowledge the worth of their warrior culture, and by extension other warrior cultures, including the American military, which they despise in all it’s forms — and that definitely includes surrogate warfare like American football.
If the Libs win this battle, they will simply choose another target. Their ultimate goal is to eliminate the warrior ethos completely, which means eliminating all forms of ritualized conflict, right down to chess and checkers.