N/S PTO rules that "Redskins" is derogatory (not a case about the NFL team but likely precedent)

I'll address some additional legal issues:

You don't have to have a registration to use, and enforce, a trademark. If the PTO decided to cancel the team's registered trademarks, the team can still use the name and claim common-law trademark protection--at least until a court squarely ruled that offensive trademarks aren't entitled to common-law protection--and this is by no means clear.

Keep in mind that trademark law exists not only to protect the owner's property rights, but also to protect consumers from being subjected to confusion or deception over the source of products and services, So a court might conclude, for example, that even if the name is offensive, it's still in the public interest to prevent others from falsely implying that they are selling authorized merchandise. That's up for grabs.

For those asking about copyrights, it was assumed for many years that obscene materials were not entitled to copyright protection (or, stated another way, that any lawsuit to enforce copyright in an obscene work would be barred by the "unclean hands doctrine") until the Mitchell Brothers won a 5th Circuit case in 1979 allowing them to enforce their rights in Behind the Green Door. Since then, copyright law has been largely free of claims that offensive materials don't get full protection (although someone did try to make this argument last year as defense after they were sued for downloading pirated porn).