Not only is it crude and a little embarrassing, the controversial new Tennessee logo doesn't meet criteria for trademark. According to the U.S. Patent and Trademark Office the red and blue box with the state's Tn abbreviation is too "geographically descriptive." That means a trademark could grant the holder exclusive rights to design elements that other parties need for general identification and use.
The offending element, in this case, is the state abbreviation:
TN is an abbreviation for Tennessee (see dictionary definition attached). The applicant is the State of Tennessee and the place of business is in Tennessee. Therefore, it is reasonable to believe that the services come from and are offered in Tennessee.
Under U.S. trademark law, geographic terms or signs are not registrable as trademarks if they are geographically descriptive or geographically misdescriptive of where the goods/services originate. The theory is that other producers in that area would need to be able to use a geographic term to describe where their goods/services are from and that one person should not be able to prevent others from using that term.