I doubt that the anti-gun family members that I have, who hate the NRA as evil incarnate, could hate them any more than they already do. But getting the NRA material in their mail there is a tiny chance, but still possible, that they would actually read some of the material. These relatives believe that the NRA is encouraging people to go out and shoot others, that it wants it to be legal for children to buy machine guns, etc. When they see that the NRA is in the business of protecting our constitutional rights and promoting gun safety then they might not hate it quite so much.
But as others have stated, the anti-gun crowd does not want facts and reason. They are reacting emotionally. So, for example, when they demand that "something be done" after a mass shooting, I have often said to them "what specifically do you think a new law might accomplish that would prevent another mass shooting" they will say "ban all guns", "Confiscate all guns" or things like that. When I point out that this will not happen, and how would they handle the reality that there are hundreds of MILLIONS of guns already in this country, and that those in the hands of criminals are already illegal and that there is no chance that these thugs would surrender their guns just because of a new law, the anti-gun people just refuse to answer or deal with this reality.
So since I know I will not change their minds about it, I can at least enjoy annoying them. On the other hand, if they are open to learn even a little about guns and gun safety, there is hope. I worked with a woman who didn't hate guns, but was fearful of them. I convinced her to have her and her husband join me at the range after I gave them a "class" on how guns work and how to safely be around guns. They now are active shooters and enthusiasts. Its my only success story in this area but one is better than none.