I don't think there is any way of telling how many people resigned because of prop 8. I do know that I saw several people with information about resigning at the SLC Temple protests that followed prop 8. The people that I saw that had said info were all busy.
To be frank though, formally resigning was simply a formality though. I stopped believing and going to church years before that.
Prop 8 for me was the church infringing upon the rights of people who were not members of their church. It's one thing to micro-manage and force dictates to their own members...but to actually take-away the rights of someone who doesn't even share your faith is what made me want to finally cut ties.
+1 We've been on the fence for a long time before Prop 8; but after I heard about the forced "fund raising" with tithing information that was a guarantee the church would never see another penny from me.
What did provide one of those proverbial last straws for me was how they told members to support it financially and then pretended that the money came from the Catholics and other groups.
They also did the same thing over in Maine, where the SP and the BPs had their wives head up the movement sending mass emails and then again claiming that they were merely supportive, while trying to redirect the criticism to the Catholic church, who had the integrity to at least take out full page ads asking for money to fight it.
The mormons working with the NOM folks then tried to get the courts to keep the names of the contributors from being made public. Meanwhile the other groups were taking the heat from the LGBT for their contributions.
Later I was told that the reason that the LDS did this was because they knew they would be singled out for persecution, just as they had always been. Nope- it was because they are cowards who fear being found out more than anything else in this world.