It makes sense if you understand that they aren't focused on general principles. Diversity is bad when it involves non-whites, women, gay people or research involving these groups. Diversity is good when it involves "race realists." Free speech is bad when students are advocating for divestment initiatives. Free speech is good when a professor calls somebody the n-word online.
The goal is white supremacy and antifeminism.
The goal is power. Suppressing DEI, etc is just a simple way to find a group of people that have different values and eliminate them from the power structure.
An important part about targeting DEI and trans communities is that these two groups stand for immutable properties: I can’t change my race. I can’t stop being my gender identity.
When you “other” people based on immutable properties, it becomes very dangerous. If you can’t force someone to be white and straight, what do you do with them? The government stops funding programs to help these groups, they spread lies and fear about them, and then they sit back. When the people in power tell their supporters that the “other” are the enemy, what recourse is left for one’s safety other than violence. Authoritarian regimes always trend towards genocide, and they always target groups with immutable traits.
When these people use "freedom of speech" all they mean is they want to say their vile Nazi stuff without people complaining.
Also called freedom from consequences. Free speech makes sense in a free society, freedom from consequences does not. Yet that's what they're calling for.