The irony of people insisting that a lack of empathy on this topic is the problem is quite funny to me because as a normal person you can't actually identify with what a trans person feels.
Nor a person of another gender. Nor a person of another race. Nor a person of another culture. Or just any other human being in general. This is fundamentally xenophobic argument. "They are different, therefore, I cannot know how they feel," has been used as an excuse for some utterly horrible things.
The entire function of empathy is projection of your own emotion onto another entity based on extrapolation from common factors. You don't need to be dissatisfied with your biological sex to know what it's like to feel like an outcast, to be questioning if anything that happened to you is result of you being different, and so on. We all have these core experiences to some degree or another. None of this is completely alien. Only the circumstances are different. This is why empathy works at all between any two human beings. And trying to raise walls based on differences, saying that empathy cannot apply, is exactly what allowed for every single genocide we've seen. You don't want to be in that camp.
You haven't followed the trans activist arguments closely. What they ultimately want is for their definition of gender to be synonymous with sex. You may think that's not true and they claim that the two are not the same but in actuality they do want those to be the same because they insist that asking whether or not someone is a biological male or female (which is relevant for many reasons) is some sort of aggression. So in essence they are asking everyone to just pretend that a trans woman is the same as a biological one for all intents and purposes. There are already trans activists that think that preferring biologically male or female partners is discriminatory as if someone can be entitled to sex or something. These ideas don't exist in a vacuum.
And religious activists want creation to be taught in school. And gun activists want to drop all regulation. And don't get me started on lobbyists from corporations.
You are taking the views of a tiny minority, really, really tiny minority, which just happens to be particularly vocal, and projecting it on general population. Spend some time actually talking to people representing minority groups. Not the few aggressive ones you meet on the internet, because they are statistically very likely to have extremist views. That's why things they say catch attention in the first place. But with people you meet randomly, where maybe you didn't even realize at the first glance that they hold to a particular religion, culture, or gender identity. Because right now, you're not even talking about real human beings. You are operating with stereotypes. Vile, xenophobic stereotypes. There are a few people who match these stereotypes, absolutely. There will be people who match any stereotype, no matter how horrible. But if that's what you gauge people in general population by, you are just a bigot hiding behind a facade of false logic.
You can say that you think people should be treated equally all you want, but they aren't. This is exactly the same situation that's currently unfolding in Russia, for example, with treatment of homosexuals. Government officially supports equal rights. But at the same time, enacts laws banning "propaganda of homosexuality," which in practice means that these minorities cannot defend themselves. They are not allowed to do things as simple as hold a rally, or print educational information. So while the law says they are all equal, the society grows ever more toxic, and in practice, crimes are constantly committed against minorities, and police do f*ck all.
This is a somewhat extreme case, but transgender individuals in many of the first world countries are going through the same problems. They have to organize and they have to try to push through some sort of a coherent platform. Because average person simply isn't familiar with any of these issues. And from ignorance comes xenophobia and often violence. And instead of showing a bit of empathy here, you are attacking the very attempt to self-organize on the basis of a few individuals who've exploited the voice they've gotten to spew nonsense. Moreover, you try to push that through under guise of enlightenment, when your entire position is based on a very narrow view, bad stereotypes, and limited information.
And I can tell you all of that with certainty, because a few years ago I'd be inclined to agree with you. Because I was also exposed primarily to the same garbage of information you have. Since then, I've met a number of transgender individuals at work and in various communities, some of whom I'd never guess were transgender if they didn't acknowledge it. Absolutely none of them were radical. And yet, absolutely each of them has experienced an undeserved quantity of bile from all manner of people. And this will keep happening if we don't start talking about this on a more even footing and with a lot more empathy. We do need some formal declaration of transgender rights in law. We do need to establish some norms and terminology, even if it seems unfair and arbitrary. We've had to do this to fight racism. We've had to do that to fight homophobia. And we'll have to do it again if we want to live in a world where transgender individuals aren't subject to violence and harassment simply because of how they feel. Suck it up. It won't kill anyone to learn a few extra pronouns and be more careful with their use. Ignorance you're trying to promote, even unwittingly, does.