Do you have to be heterosexual to be a Christian? For Methodists, the answer may be no if you're talking about joining the church. Many Methodist churches have accepted non-heteroes into membership--even if they admit who they are.
Does somebody have to be heterosexual to be ordained as a minster to the church? Obviously, or maybe not so obviously, the answer is No as long as you keep quiet about your sexual proclivities. But, Yes, if we modify the question to Can you be ordained in the church if you are unwilling to keep quiet about your same-sex relationship?
Christians have long been in disagreement, sometimes in torment, over the public acknowledgment of minister's sexual behavior. For example, married men (or any women--married or unmarried) cannot be ordained as a priest in the Catholic church (except for those situations in which an exception is made; e.g., an already married Episcopal priest moves converts to Catholicism).