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.
I'm familiar with the phenomenon. You see it in abundance in wealthy, liberal, urban areas with concentrations of homosexuals. The parishioners are the biggest drum-beaters and petition-signers in the world—but the petitions tend to be for socialism or diversity or whatever is irrelevant to, or at odds with, normal moral life. That's why I assume bad faith until shown otherwise. Liberal areas are littered with pastors and parishioners who are hijacking the name of Catholicism to steer it toward self-important dissent.
Your post before touched on the core of the issue:
These are immortal souls starving for sacraments - not a civic matter.
It's no longer a distant civic matter when the civis is coming to get you. For a Christian, not to stand and fight is cowardice or treason.