Establish a nonviolent group. That's how. PFLAG was started by someone who thought, well, I want a support group for GLBT's. Start a group that preaches nonviolence. Start a group whose message isn't shoving gay-rights down people's throats, but instead asking for equal rights, regardless of sexual preference. Start a group that shows its members are people. Not gays, or lesbians or blacks or white, just people.
You might also consider coining a new name for people with same sex attractions. Rather than using the word gay, maybe if we called ourselves something else. The word gay has such a negative connotation these days, people use it in the phrase "that's so gay." If we disasociated ourselves with this term mayber that would help.
The best way to build a brick house is one brick at a time. Start small. With prayer God will help your group grow, people will learn about it, and sooner than you think you will have a movement. One that might be more successful than any so far.
And if you want any help... you know where to ask.