I'm a big supporter of the NRA, TRA and our second amendment rights. I read the proposed bill and see nothing that infringes on our second amendment rights.
What I do read is legislation preventing mentally impaired people from owning a firearm until such time as they can prove themselves mentally competent. As a responsible gun owner, I have no issue with sane people owning guns, people who have mental issues have no business with one regardless if they're a veteran or not.
Unless I've missed something (in which case please point it out) this is the responsible thing to do.