In the name of Allah, the Most Merciful and Compassionate
Can you be gay and Muslim? The simple answer is yes but this needs explanation.
In Islam, there is a hierarchy of sins, There are sins for which if a person commits, will no longer be a Muslim and would be declared an apostate. An example of this and also the worst sin a person can commit is engaging in Shirk (Polytheism). For this person to be considered a Muslim again, they would have to declare their faith again and its basically back to square one.
There are sins which are classed as major sins but they do not take you out of the religion. However engaging in them continuously without any remorse for violating the commandments of Allah (Glorified be he) puts you on a dangerous course that increases the chances of you ending up as an apostate.
Now let me not sugarcoat things here. It is explicitly clear from the two main sources of Islamic Law (The Quraan and the Sunnah (Rulings based on the actions and sayings) of the Prophet Peace and Blessings Be Upon Him) that acts of Homosexuality are strictly prohibited and in fact Allah (Glorified be He) destroyed an entire nation for engaging in this act. However it is acknowledged that individuals might have homosexual tendencies, provided that they don't act upon it, Allah (Glorified be He) will hopefully forgive them and admit them to the highest levels of Paradise. The challenge comes when you have deviant Muslims claiming that is ok to be Gay and engage in Homosexual acts when it has been made explicitly clear that it is not.
The conclusion that we come to is that being Gay does not take you out of the fold of Islam. Being Gay but actively declaring you are gay and claiming that in Islam is ok with it makes you a MAJOR sinner in the sight of Allah (Glorified be he). Lastly being gay, but striving to restrain yourself from engaging in homosexual acts could in fact grant you the Mercy of Allah (Glorified be He) and you will be rewarded and forgiven. The rulings of Islam are clear as have been stated to us by Allah (Glorified be He) in the Quraan and His Messenger whom He sent as a source of guidance (Peace and Blessings be Upon Him). It is not upon a Muslim to interpret Islamic rulings in accordance to their desires, accepting what they want and discarding what does not align with their desires. You either take it all or leave it.