Homosexuality is a clear and open sin according to Islam as well as all divine scriptures. Allah created man to marry woman and vice versa. Marriage between the members of same sex can never be allowed in Islam. The ruling of marriage of transsexuals is given in another answer.
Although homosexuality is among the worst kinds of disobedience to Allah's commands and a clear sin but a person who is guilty of committing this heinous crime does not become Kaafir or disbeliever simply by committing this sin. However if someone believes that homosexuality is permissible and lawful in Islam then this amounts to disbelief and Kufr. Hence, someone who believes that homosexuality is permissible in Islam will become Kaafir on the account of denying the clear teachings of Allah and His Messenger Sallallahu Alaihe Wa Sallam.
The conclusion of above answer is that a sinner can remain a Muslim as long as he/she does not accept the sin to be permissible and lawful.
Therefore homosexuals, heterosexuals, transsexuals can be Muslims and can also be non-Muslims.
And Allah knows best.
Mufti Ikram ul Haq
Fatwa Center of America