I think the way to approach this is to ask them what they think it means to say a human has changed sex.
What do they think sex is, exactly?
No trans woman has ever had a baby, or ovulated, or even had a successful uterus transplant. (The one time this was attempted, the patient died.)
No trans man has ever produced sperm.
No person has ever changed their chromosomes.
If they don't think that's what sex means, what do they think sex means?
I once had someone on Twitter ask me to "define female without referring to genitals or reproduction". She got absolutely rinsed in the replies.
So I think the key to answering this question is to quiz them on what they think changing sex actually means. Because they won't be able to name anything a trans person has ever done which isn't completely superficial.
Taking cross sex hormones might have a physical effect on your body, but it doesn't make you capable of performing the opposite reproductive role. Same with surgery. Having a vaginoplasty might enable you to have penis in neovagina sex, but the sperm has nowhere to go. Having a phalloplasty might possibly enable you to penetrate somebody else, but you won't be at risk of getting them pregnant.
So until it is possible to perform medical interventions on trans people which actually enable them to perform the functional, reproductive role of a member of the opposite sex, I think it's fair to say that humans can't change sex.
The comparison with being gay doesn't hold up because obviously it is biologically possible to be attracted to members of the same sex, because some people are in fact attracted to members of the same sex. It is self evident. The fact that it is even a point of discussion is proof that it is possible. Unlike changing sex.