It’s a very important question – and I think the answer is a lot more complex simple hatred of trans-folks, though that is evidently part of the problem.
The conflation of many separate issues into one catch-all question may be part of the issue. Trans-people existing and being part of society is a separate issue from trans-people taking part in competitive sport. Not because there isn’t a solution that can be reached, but that solution needs some careful thought before it can be implemented.
When issues are conflated and the rejection of one aspect becomes a rejection of the whole – then dialogue breaks down. The vast majority of people when considered one-on-one are inclusive and good natured, but inflamed rhetoric on both sides is causing problems that are group based.
There are a number of different discussions that need to happen in order for society to move to a place where trans-people are safe and feel safe. Those discussions aren’t easy and the further factioning happening in the LGBTQ+ community is indicative of groups arguing for their subjective version of oppression as paramount. Ultimately members of each group are the ones that will suffer.