Do you accept that some people firmly believe they are born in the 'wrong' body?
Accept that they believe it? Yes, in some cases. Accept that it's true or that people ought to 'be kind' and behave as if it's true even if it isn't? No. To me it's a belief on the same level as believing Jesus Christ is your Lord and Saviour. I will accept the belief; I will support your right to hold the belief, but I will reject very firmly any attempt to coerce me to speak or act as if I too believe it.
and have a right to live as the other sex
This is meaningless to me. If it means 'live according to culturally masculine or feminine stereotypes and claim this makes them the opposite sex' then they're free to do so but I'd find it offensive. Much as I would if someone claimed to 'live as another race' by enacting racist stereotypes.
possibly taking hormones and undergoing surgery?
If they pay for it themselves, it's none of my business. I don't think taxpayers' money should be spent on any of it. I'd support NHS counselling for people suffering from gender dysphoria.
Or do you believe these people should not ever be supported to live as the opposite sex? That doing so is always wrong?
Not wrong so much as impossible. I don't think anyone can 'live as the opposite sex' so I think that 'support' which tells them that they can is ultimately unhelpful.
A few years ago I'd have said that if you're a man who wants to wear a dress and makeup, go ahead, nothing wrong with it. I still think men should be free to do this without harassment. However, I no longer think it's the equivalent of a woman wearing trousers, because of the number of men for whom it is fetishistic. If dressing up in any outfit is a fetish for you, do it in your own home, not in public.
Needless to say, no male person, however they think of themselves or whatever modifications they have made to their body, should be in women's spaces. Even very nice harmless men. My dad is a nice harmless man but I wouldn't bring him in women's facilities - because although I trust him completely, to other women he's a total stranger. Women's spaces aren't prizes for men who are nice, or feminine, or vulnerable. They're for women.