If someone were to tell me (hypothetically) that he is a unicorn, he would be in effect be asking me to participate in his fantasy world. However, if a post-operative male-to-female transsexual tells me that she is a woman, that is not a fantasy, that is a reality that has been brought about by the use of medical science. And even if people who are physically male tell me that they consider themselves to be female, that is not really a fantasy so much as it is an aspiration they have. They could never really become unicorns, but a sex change is an option in the real world, not a fantasy.
Ultimately, it is wrong to accuse transsexuals of not knowing who they are. They know who they are. They are just different from what some people think they are. And really, it is reasonable that we should all get to live our lives as we choose, rather than as someone else might choose for us. The video of the lawmaker from SD opens with the claim that he wants to "protect the children". Protect them from what? I suppose, protect them from the possibility that they too may someday wish to become transsexual, as if everyone can just be forced into conformity and then there will be no problem. This is precisely the same motive that exists for the intolerance of homosexuality, as if no one would be homosexual if we just didn't let them.
It is actually just as easy to regard a transsexual as being the gender that they claim to be, as it is to regard anyone as the gender that they claim to be. This does not impose any kind of special requirements on anybody. What, really, is the problem? Are you worried that you will be forced by social etiquette to hold doors for people who are not legitimately entitled to have doors held for them? Lots of people don't hold doors for anybody. While others will hold a door whenever someone else might benefit, without regard to gender.
More likely you are worried that people will use the wrong public restrooms. But you know, transsexuals do the same things in those restrooms as anyone else does. They don't go into restrooms to molest people, they just want to empty their bladder. Why would this be a problem for you?
The only thing that transsexuals ask of anybody is to treat them with the same courtesy that they would show to anybody else. That is not a special privilege. That is what they are entitled to as members of society. And it costs you nothing to do it.