When I saw the thread title, I thought, "Oh, great, another bill whereby the State grants the Right, leaving it the ability to take it away."
I couldn't have been more wrong. If the bill does what you say it does, it is exactly how States should bar the federal government and local governments from interfering with the Right. Hopefully, Nebraska itself is not interfering with the Right.
Much better bill than a lot of States (including Alabama) claim protect the Right.