They absolutely have been the main force behind the timing of this push. It was the main topic of General Conference a few weeks ago and one of the most eyebrow-raising articulations of official church policy.
Given the way that the church has explicitly encouraged state legislators to shoot down recent laws it's not surprising to think they'd be pushing for this.
> Given the way that the church has explicitly encouraged state legislators to shoot down recent laws it's not surprising to think they'd be pushing for this.
And the way they've influenced voters in Idaho and Arizona recently.
To be clear, it was one talk out of ~30, not the main topic. But the talk (https://www.churchofjesuschrist.org/study/general-conference...) was unusually direct and stood out among the more common, often repeated topics like faith, temples, etc.