The Department of Justice and nonprofit 'Change the Mascot' have given up on their legal crusade against the Washington Redskins in light of the recent Tam trademark decision. In Tam, the United States Supreme Court struck down the "disparagement" clause of the federal trademark statute, which for the past 71 years had empowered the U.S. Patent and Trademark Office to deny marks that, in the subjective opinion of an examiner, were offensive or disparaging to a person or groups of people.
Since 1992, various legal challenges to the use of the name "Redskins" by the football franchise the Washington Redskins have been raised. In 2014 the USPTO cancelled the registration for the Washington Redskins under the now unconstitutional "disparagement" clause. The earlier denial of review by SCOTUS will be reversed now in light of Tam, and the Washington Redskins will be able to re-register the previously cancelled registration.
It is important to note that losing federal registration (as the Redskins temporarily did after their mark was cancelled) is not a loss of common law trademark rights. Trademark rights are derived from ancient common law and are among some of the oldest historically recognized laws. The earliest examples found by legal scholars include records in Egypt of branded cattle and disputes between farmers about source identification of cattle products.
The loss of federal registration for "Redskins" was not a loss of brand source identification for the Redskins nor a loss to the right to use and protect their use of the name, as consumers continued associating the name of the franchise with the team and the team continued using the name anyways. The only "loss" to the team was some of the powerful federal remedies available to as a holder of federal registration, the benefits of prior notice to others in the marketplace (should a bad faith infringer use the name [though, with a mark as famous as the Redskins, the notice argument is basically irrelevant in this case]) and incontestability in court. The pragmatic result is that cancelling or denying the trademark registration of offensive words does not reduce source confusion in the marketplace for consumers, but has served rather as an (expensive) form of public relations for the groups arguing against the use of these names. (And to some extent this applies to the Slants as well, a band I had never heard of prior to these cases).
Whether the Redskins name is actually offensive toward Native Americans as a cultural or ethnic subgroupor whether the Slants is actually offensive toward Asian Americans as a cultural and/or ethnic subgroup misses the point entirely.
Whether these terms should or should not be seen in American culture as "offensive" is one that requires a dialogue of equal players and education on parts of all in the free marketplace of ideas that is of paramount importance to our democracy. It should not be left to subjective government decree.