The division comes from the generations of bigotry and hate that has fostered against these people from the beginning of time. The pushback that y’all get is a fight to foster an environment where they aren’t considered freaks or degenerates. The issue I have with many on the Right when it comes to human rights is they don’t show compassion for the other side. The don’t acknowledge their plight and show any concern for helping. We see this with Trans, gay, and even border security. All their policies and arguments are for blocking the interests of minority groups and some of their concerns are totally valid like the locker rooms and sports issues you bring up. The problem is they hardly ever balance their opposition with ideas to promote inclusion and acceptance and a safer more understanding environment for these people to live in.
Let’s take you specifically, your major issue are sports and locker rooms right? You just said if it’s simple “social” the it’s not much concern to you, right?. But then you bring up their pronouns as an area of pushback. You could easily balance your sports and LR opposition with something promoting or showing understanding for pronouns which is social acceptance. Why can’t you do something as simple as that?