Reactionary Culture Warriors Are Not Friends of Free Speech
Nor should they be called conservative at all
The 'anti-woke' movement has long prided itself on defending free speech, against postmodern critical theories that justify the severe limitation of free speech via an oppressor vs oppressed worldview. However, in recent years, the anti-woke movement has been hijacked by reactionary culture warriors, who care less about free speech than about them winning the culture wars. Their worldview is much closer to neoreactionism than classical liberalism, essentially. All their talk about 'common good conservatism' is neither about the common good, nor about conservatism (when did massively expanding government power become conservative?), but rather window-dressing for a neorection-like project. This authoritarian-reactionary approach to politics is prominently on display in Ron DeSantis's Florida, home to the infamous 'Don't Say Gay' law and the associated War on Disney.
For example, regarding 'Don't Say Gay', they said it was only about preventing inappropriate topics from being taught in elementary schools, notwithstanding the fact that it has since been extended to older students. Now, some in the Florida Republican Party want to take it further: a new bill, HB599, would prohibit a government employee from providing their preferred pronouns to their employer. Yes, you read it correctly. This is a bill that would prevent an act of free speech between two adults, no kids involved! The reactionary right fundamentally wants to control the behavior of adult citizens, to achieve their religiously motivated vision of the 'common good'. This is called theocracy, and it has historically been the enemy of both classical liberals and the genuine Burkean conservatives who defend our long-standing values.
Now, let me clarify that I am actually not in favor of making routine the practice of 'sharing pronouns'. It makes conversation clunky, and it is unworkable on a large scale. However, there's a big difference between disagreeing with someone's speech, and banning it by the force of law. In general, I think most people would agree that speech that doesn't put anyone in danger should not be banned. You might or might not agree with the practice of sharing one's pronouns, but it clearly doesn't put anyone in danger. This means banning the practice of sharing pronouns is a major violation of the long-standing free speech norms of Western society. This is why we should not enable right-wing culture warriors to steal the conservative label. Every time they try to call themselves 'conservative' we should push back hard. Words have to have meaning, and 'conservative' should not mean neoreactionary or fascist.