The respect that's being called for is in the first place one of basic human decency. It doesn't matter what you think of it. Calling someone a "freak" with the contempt it is obviously meant to convey is a Victorian attitude and should have long since been shot. Then there's the second point that transgender people -- again, whatever you think of the topic -- have the right to live and exist within society without fear of the sort of discrimination and abuse to which they are, directly or indirectly, subject to. And thirdly, as has been pointed out several times already, the "transgender" part refers to a person's gender identity, and in that regard there is no pretence whatsoever. People are who they are.
Belief is a larger step, I will admit, but to some extent at least it is merely that the change from transgenderism being something that was underground (and anyway very difficult) to being very much accepted and public has taken place so quickly that society has barely been able to adapt. But there is nothing new about it, and it is, if anything, a more recent concept to insist on the idea that gender is binary than to accept the existence of multiple possible gender identities.
It's unfortunate that English uses "man" and "woman" to refer both to the biological sexes and, increasingly, to the gender identities. By now, though, there's a huge body of evidence from across the world that gender identity is not and never has been so clear-cut.
As to the court case, I thought the judge in the earlier hearing made a fair point in arguing that the labels on birth certificates are referring to biological parentage, and ergo this person is the child's mother in the context of the certificate. Unless and until the law changes explicitly, to change the point of and information on a birth certificate, I am not sure that Freddy can expect to win their case -- and, even in the event where a judge agreed in principle, it might end up in a similar way to the rather sad case of Owens v Owens, in the context of divorce, when judges ruled that yes, the situation completely sucked for the unfortunate Mrs Owens, but there was nothing they could do within the law as it stood (ditto abortion in Northern Ireland, albeit for more technical reasons).
As a further point, I don't think it's right to say that "no amount of surgery", etc, will change the fact that women (who were born that way and with a functioning uterus) are the only people who will ever give birth. Uterine transplants are difficult but not impossible, and a few babies have been born -- albeit to biological women -- from surgically transplanted wombs. I don't wish to give the impression that I am looking forward to it, but the day may not be far off when transgender women (ie, people born male) are capable of giving birth.