This is basically what happened with abortion. The supreme court overturned Roe v. Wade and the Republican argument was that it was just a "State's rights" issue but then introduced a federal bill to protect the "preborn"[0] recently. It's fine until states do what they don't like.
> • Include “pronoun:” under “name:” in name tags and introductions in groups as an opportunity for participants to make their pronouns visible. At the beginning of the semester, educators can call out students by their last name instead of their first name in case a student has not been able to change their name in the Student Information System or legally. Let students know that after class they can let you know what name they use if it is different than what is on the roster.
> • At the beginning of the semester, educators can pass out 3x5 notecards to students and ask them to add their name, pronouns, and whatever information you feel is necessary to know about the student that they might not want to share out loud.
> • Have pronouns be added to all email signatures, and link the word “pronouns” to this guide or another reference for people who are new to this practice:
‒ Sincerely, Mx. Marvel Pronouns: They, Them, Theirs
Granted, part of the document talks about not having to share your pronouns, but we don't know what kind of internal policies they had that employees either needed to follow or at least felt pressure to follow.
It isn't really 'personal liberty' being removed in this case. This is a bureaucracy that is enforcing external appearance standard. I'm sure these folks will be free (!) to express themselves however they like in their personal lives.
0: https://www.congress.gov/bill/119th-congress/house-bill/722