Today's decision in Gilliam v. Gerregano (Tenn. Ct. App.) so holds (in an opinion by Judge Kristi Davis, joined by Judges Frank Clement and Neal McBrayer). This means that any restrictions on such plates can't be viewpoint-based or too vague, though clear viewpoint-neutral but content-based restrictions might be permissible.
Whether plaintiff can keep her 69PWNDU plate was thus not resolved, because the appellate court sent the case back down to the lower court for further proceedings. (The lower court had concluded that the license plates were government speech, and thus that the government's decision to reject a plate was completely unconstrained by the Free Speech Clause.) The appellate court's decision is in keeping with the trend among other courts, see, e.g., here, here, and here; those cases conclude that, while the designs of license plates are government speech, even when the government allows lots of groups to submit designs (see Walker v. Sons of Confederate Veterans (2015)), the letter and number combinations on personalized plates are private speech. For a contrary view, see here.
Here is the appellate court's summary of the state's policy, which will now be evaluated by the lower court: