If the conservative platform has devolved to dog-whistling or outright hate speech, calling for interstate armed conflict etc... then yea it's gonna seem like an "anti-conservative" bias.
Since you didn't make it past that part, I'll save you the trouble. The case so laughably lacks legal merit it's already a joke.
What exactly is hate speech? There are some people out there who think stating clear biological reality about a certain topic is the most vile hate speech imaginable, yet others would call that same behavior stating clear scientific fact.
Or better yet. Have you ever played the “______ is racist” game? Search literally any noun and “is racist” in a search engine and you’ll find references to virtually every human activity being called racist at some point or another: including gardening, hiking, and milk.
If anything can be labeled as hateful when convenient, the conditions for honest discourse online seem to become impossible.
If your "clear biological reality" is denying the existence and experience of transgender people, that's hate speech.
If it's claiming that black people are less intelligent, that's hate speech.
If it's claiming that Native Americans are naturally lazy, that's hate speech.
There have been a lot of "clear biological realities" down the centuries that have been used to justify the continued oppression of minorities and marginalized groups. As long as they're not causing harm to others, every human being deserves the same level of dignity and respect as every other, regardless of what you or anyone else thinks of their identity.
To clarify, it seems like you're arguing a strawman (or strawwomyn) argument with your (IMO very bad) points.
To pick a less contentious example, I think science can clearly recognize that the average man is a little bit taller than the average woman. Would you agree that this is correct? In and of itself, would making this observation be bigoted?
It doesn't seem to me that doing the science and objectively recognizing that this height difference currently exists in nature is bigoted against any group. To me, it would take something akin to a law that treats people with different heights differently in society to turn a scientific observation into some kind of oppression or harm.