Haugen is not transgender, I'm not sure where you're getting that from.

For all I know Haugen is not trans. But even if she was that doesn't preclude her from not being a critical social justice (CRT) activist, so that is not the most significant fact.

What she is aiming for by censorship of "hate speech" is CRT defined "inclusion" [1]. This means to not tolerate any speech (including symbolic displays or representation) that offends, might offend, or could be construed as being potentially offensive to any member of any marginalized group.

Members of putatively marginalized groups [2] who do not claim to experience or suffer from the oppression critical social justice activists assign to them are dismissed as inauthentic.

So in the end inclusion by censoring "hate speech" is a tool to ensure censorship of any opposing viewpoint.

[1] https://newdiscourses.com/tftw-inclusion/ [2] https://newdiscourses.com/tftw-marginalization/