Ok imma just clear up all this bs because I, as a proud honourable muslim, can say the truth.
In Islam (not the fake, horrible one you see on the media) we are taught to show love and kindness to all. The Prophet (PBUH) suffered from persecution from so many, yet he still showed those who sent hatred towards him kindness. He loved and cared for everyone, no matter how corrupt their minds were.
Now, it is true that LGBT is not permissable in Islam and yes, it is considered sinful I guess. BUT, it is not our right as humans to persecute one for sinning. Ever heard the phrase "sinning on a sinner"? Thats exactly what we as Muslims are forbidden to do because everything is down to God. We must not revenge because tyat will make us just as bad.
Instead, we are to show kindness to them just as we would to our friends and family. Yes, it is good to talk to the people about it but we are not allowed to become violent with them. Again, thats all in God's hands. Not to mention the fact that those who show love to all, even those who least deserve it, are the best of mankind.
So why is the lgbt community so accepting towards us? Because of this. Because of the fact that nobody deserves to be persecuted by another. Its God will as to what has to be done to sinners, not ours. We stand as one, humans together, to fight hatred towards one another. They know the truth, and they have accepted it.
Hope that clears it all up for y'all