Ched & Ghost good points but why not just quietly go about it like the majority of others. Fight for equality in the courtroom, but keep having "pride" parades and you antagonize the opposition. Which in turns strengthens their resolve and instigates them to rally against the cause. Lull them into over confidence though apparent in action and then they fail to oppose the legal fight with enough force.
Yeah, um... no.
Along with the above-mentioned rights campaigns having done the exact opposite and having accomplished their purpose quite effectively despite that, this also pretty much screams "I don't like it when gay people brandish their icky gay cooties because I don't want to have to look at it, so they shouldn't do it". It doesn't sound like you're trying to suggest alternatives, it sounds like you're trying to stifle them so YOU don't have to hear them.
Until they stop being assaulted/killed on the basis of their sexuality and denied simple things such as human rights, jobs, services, and other glaring examples of inequality, there needs to be an active movement and a voice able to be heard. They have as much right to silence you as you do to them. So if they just sat meekly on their hands and tried to con their opposition into pity, and instead tried to go quietly through the courts, you bet your *** they'd lose momentum so quickly that it wouldn't even matter in the long run. Nothing would change.
Piggybacking on the mention of women's rights and civil rights as similar -- imagine if either of these movements did the same thing you're telling the LGBT movement to do. At the time, it was perfectly natural for women/people of color to have few to no real rights despite the insistence that they did or they didn't need any, and the general opinion was very much parallel to the homophobes and fundamentalists of today. It was perfectly normal to them, and people like that despise change. So if they had done as you suggest back then, do you really think women would have the right to vote and hold jobs outside of the "feminine" norm? Do you think we'd have abolished the "separate but equal" concept for schools and other public venues?
Why is it any different now that people who rally for a cause of equality should have to stay quiet so they don't ~disturb the neighbors~ or some stupid reason like that? There's not many groups remaining in the United States that remain unprotected or even excluded in some fashion by state and federal law... but the LGBT community happens to be one of the last few groups that is still not fully treated as equal.