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. Conservatives are more prone to this, but liberals are absolutely not immune. To exist outside the role you were “assigned” is a threat to society that assings the roles, ergo a threat to the very way of life for those who see them as innate truths.