Interestingly, I don't hear ag producers, nor their orgs, pushing for PLT. There's probably some, but I think most realize that the AUM rate on State Trust Land is a fair bit higher than it is on federal lands. Ranchers with federal grazing allotments have a sweet deal. I'm on a local working group with half a dozen ranchers/ag producers, and I never hear them calling for it. Also, years back when this issue raised its head, the Montana Wood Products Association, which is the largest voice on behalf of the state's timber industry - came out in opposition to PLT.
As to Republicans, I think most are well-meaning and see the various issues with public lands in terms of their management, and see the state lands, which by law must generate revenue and do so via mining, ag and grazing, and timber sales (all things many Republicans see as needed on USFS/BLM lands) and extrapolate that into a belief that the lands they love would be better managed under the state. There's also an undercurrent on the right, and I won't go into whether it is justified or not, that the Feds have their grubby paws into too much of our lives and that footprint should be reduced - thus PLT would be a win/win.
To say it again, most Republicans and/or PLT proponents aren't wanting a reduction in access, stake, or acres of land - they are well meaning. I just think they are being honeydicked.