"God doesn't change his mind".
First, read 2nd Timothy, 2: 15 "Study to shew theyself approved unto god, a workman that needeth not be ashamed, (and this is the important part) RIGHTLY DIVIDING THE WORD OF TRUTH".
Now, understand the meaning. "Rightly Dividing" means DIVIDING the various aspects of the scripture into its separate dispensations. This means that, for example, at one point, ALL creatures of the earth ate the FRUIT of the earth. In other words, man, lions, tigers, and bears all ate FRUIT. There was, during the events of the garden of eden, NO consumption of meat by anything. Yet LATER certain meats were declared "clean" to eat. Eventually, ALL meat was declared clean.
Another example: At one point, the only route to salvation was to be a Jew. Non jews, or Gentiles, were unable to achieve salvation, unless they became a Prostelitite (spelling?), which means "a gentile that has become a jew". According to the Bible you hold so dear, this is no longer the case in our current dispensation, the dispensation of grace, the route to salvation lies only in admitting to being a sinner, that one cannot save oneself from god's wrath, and to trust in the salvation provided by Jesus.
There are many cases where "god" changes his mind in the bible. I am not arguing the validity of the bible here, merely making a point that you have NO FUCKING CLUE what you are talking about.
But you ARE right about one thing: the Bible (a religious text) does state that same sex coupling is a sin. But that fact is a religious one. And so long as we live in a nation of....yep, you guessed it, RELIGIOUS FREEDOM, and the actions of these people do not infringe upon your own rights, YOU have ZERO right to require that other people adhere to the constructs of your faith.
I am immensely happy for the LGBT community, and I wish you all the best, but you have a looooong, hard road to walk. It will be full of hate, discrimination, hypocrisy, and laws that say one thing while another is enforced. It will challenge you every day of your lives, and will do so for decades to come, and will not stop doing so until every last vestige of intolerant thought is gone from human minds. However, it is YOUR road to walk now, so get to marching, and best of luck....