I really do not see the equivalency between a government database and something compiled by a private organization, whether it is Facebook, Google or the NRA. If NRA members object to its practices, the organization will need to change or lose financing, support and members. In that, you may have something you can construe as a victory.
I'm generally not a fan of government lists, and it certainly has nothing to do with guns. Maybe it's the fact that I'm part of a family that included Holocaust survivors, or my studies in American History involved the McCarthy Era. As a general rule, I believed most other liberal similarly disliked government lists. Heck, if your name just sounds like someone else, you may be on a list that makes it difficult to board an airplane. I do not make an exception for lists of gun owners who have not committed any crimes.
Additionally, I have no idea what the position of the NRA is concerning the offender list. I first heard about it tonight when I read the OP. I also am not an NRA member, and they receive little coverage or attention here in NYC. I would not be surprised, however, if they opposed the list, as they generally take a more absolutist position due to fear of the "slippery slope." This fear is not entirely unjustified as many in this forum would use such a law as a stepping-stone to enact further gun control.
As for myself, I'm more of a compromise sorta guy. I have no problem with the offender registry or universal background checks. My good nature does end well before an assault weapons ban and magazine limits.