Fr. Marcial Maciel, Founder of the Legionaries of Christ, was pulled from his post as Director General of the order in 2006. He was ordered to cease all public ministry (i.e., "shut up"), and devote the rest of his life to prayer and penance. This was on account of his long history of moral problems, which included sexual misbehavior. You may not agree with this course of action (I don't have a problem with it), but "this" is indeed what the Church sometimes does to enforce moral discipline and protect her flock from abuse and bad example.
The homosexual "marriage" campaign, like Obama's insisting on Catholic subsidy of abortion and contraception, is part of Leftists' cultural and political campaign to silence their opposition. Priests with no stomach for the fight are unworthy to act in the Person of Christ. They have signed on as priests to defend the Faith to the death, if called upon. The occasional petition drive on a clearly moral issue seems a pretty small mortification by comparison.
If a priest has drawn souls to his parish based in part on his unwillingness to raise certain issues and lead his parishioners amend their lives, he is not helping them. By creating an environment that confirms them in their errors and sins, he is leading them to moral and psychological ruin in this world, and worse in the next. These parishioners can and should be absorbed by other parishes, where there might be priests who are less timid and less concerned for their own comfort.
Today, we are being ordered by the secular State and its culture to sacrifice to its gods of abortion, sexual deviance, and divorce. As in ancient Rome, the State will eventually harass and execute some of us for having the nerve to disagree. If we face this fact, things become clearer. And God wins in the end. It's His game.
You appear to assume nothing but bad faith on the part of pastors of parishes that are not participating. In at least one parish it was a decision taken up by established parish council - not the pastor. Another parish said they wanted no political intrusions of any kind into their churches - to segregate the sacred from the profane has very old foundations. Most of the parishioners will likely sign but do it elsewhere. They go to church to receive the gospel and the sacraments - not to sign petitions of any sort.