Would you vote for a Democrat?
I’m not a single issue voter (usually), so I vote the party ticket unless a Republican strikes me as a scumbag. I cannot recall the last time I voted for a Democrat. However, I clearly identify myself as a Republican, so I vote for Republicans.
If I were the NRA, I would have to identify myself as a Republican arm if I only voted for (endorsed) Republicans. I could no longer claim to be a single-issue advocacy group, becaue I’d really only be advocating for the Republican party.