Why does it seem most people, mainly conservatives, against Trans people? Unless I am wrong I never heard of one shooting up a school church or whatever. The ones I have met have been pretty cool.
People fear new unknown things (as perceived by the individual), especially when it comes to bodies and human form, instinctively.
It doesn't conform to their strict societal standards as crafted by thousands of years of culture and history. The authorities have always persecuted and cracked down on anything that threatens the patriarchal standard.
Minorities make the easiest targets. Trans people are an extreme minority.
Some people think it has more to do with sexuality and sexual urges, so their perception is that it is perversion.
Projection is also a common way for people to deflect blame for societal ills. Religious zealots will ignore and even shield sexual abusers present in their own institutions and divert that animosity to outside groups that make convenient targets. They are ok with the abusers within their walls because they are seeking absolution through religious systems. They are not ok with queer people because they need to scapegoat a group to explain why things don't seem to be getting better.