The church mostly tolerates people merely having, and even actively pursuing, contrary political beliefs. There’s lots of progressive Mormons in SLC who push non-discrimination ordinances and such and are largely ignored by the church. It’s when they end up directly criticizing and directly opposing the LDS leadership that they bring the hammer down. That’s what happened with the ERA group woman-- she didn’t just support the ERA, but actively spoke out against the church’s support of it. She ostensibly wasn’t excommunicated for supporting the ERA per se, but for denying that the President/Prophet had really received a revelation from God commanding church members to oppose it.
I do think the church is a little more politically-savy these days. For example, they’ve toned down the notion of the President actually receiving direct divine instructions regarding particular political issues, which means that simply holding a contrary political viewpoint is no longer heresy on its face. In the infamous Prop 8 letter, the President merely said that Prop 8 was contrary to church teachings and that church members should oppose it, not that there was a divine revelation commanding it. Doing things that way gives a little more leeway for the church to tolerate different political opinions as it tries to be more cosmopolitan and appear less authoritarian
So it seems to me that there’s a lot of room for this new group to work without coming into direct opposition to the LDS leadership. Again, in the Prop 8 case the church tolerated individual Mormons opposing it, but only started threatening excommunication with Mormons who were speaking out against the church leadership itself. I do suspect that after the fallout from Prop 8, the church will try to be even more subtle about opposing gay rights in the future, which will make it easier for pro-gay Mormons to operate without coming into direct conflict.