I see a lot of mostly correct answers here, but as a trans person myself I can’t help but feel they are all missing the core concept.
People hate trans folk for the same reason “get back in the kitchen” is still said to women in any non-“traditional” role or the “angry black man/woman” is said about anyone advocating for their own rights. There are strict gender and racial roles that are enforced by our society so rigidly, that many have assumed them to be naturally correct laws of the universe. Anyone existing outside of those roles is seen as either mental illness to be corrected or malicious evil-doers wanting to cause trouble.
When in fact the reality is much simpler, that being human is a more diverse expressive and dynamic experience than those holding on to those “natural laws” would like to admit. To exist outside the role you were “assigned” is a threat to society that assigns the roles, ergo a threat to the very way of life for those who see gender, sexual and racial hegemony as innate truths.
Conservatives who hold high tradition are naturally the first to speak out and seek to regulate us back in to “normal society” via legislation but liberals are absolutely not immune. To reduce transphobia to a political wedge issue, while correct, doesn’t quite explain the more innocuous yet quite prevalent transphobia inside left leaning spaces.
This is factually wrong.
Trans women on HRT statistically have far less testosterone than cis women, purely for the reason that it is a hormone all humans create but trans women are actively suppressing it.