So, could a lesbian have a trans woman as a lesbian partner, or a gay man be with a trans man? Of course. If they fancy each other. First and foremost, we need to recognise that trans women are women, and trans men are men.
Look, any adult can sleep with any other consenting adult if they wish to. That should go without saying.
But I find this view so homophobic. Let's go back to when homosexuality was illegal. People risked being imprisoned if they slept with someone of their own sex. They risked financial ruin and social ostracization. Some homosexual people underwent horrendous medical treatments to try to 'cure' themselves of their desires, like cauterizing their urethras and having bleach put in their eyes because the consequences of being gay could be so serious.
If homosexuality was just about being attracted to the same gender, historically, gay men could have sought out a masculine woman/transman for a partner (if you say that being trans is innate and fixed, then the Victorian period had lots of transmen walking around having to just get on and wear dresses, etc). Never mind what that person's sex was (female). They could have cracked on and had fulfilling lives without risking their safety. There wouldn't have been anymore near the amount of misery there was. Society wouldn't have blinked, would they?
It is so profoundly insulting to all the gay and lesbian people who had to live double lives and risk their safety to have sexual relationships to say that homosexuality is about same gender attraction. I don't understand why more people can't see that. Very very few gay men (whose sex is male) are ever going to accept a transman as a partner. It will just never happen. Because it's about same sex attraction. And humans can discern sex very easily.
If you want to say a transwoman is a woman, if you want to change legislation based on that, you have to come up with some concrete evidence as to why they are. Feelings are transitory, subjective and invisible.