Maybe they would maybe, maybe they wouldn’t, but I would not be surprised if the NRA supports one of the Rino’s.
I quit the NRA years ago when they supported a number of Democrats, based solely on their 2d Amendment rhetoric all of whom wound up party loyalist voting in support of gun control.
That makes 2 members the NRA lost, I got out several years ago when my shooting buddy had his SS Colt Anaconda .44 mag stolen. Those guns haven't been made for several decades and they're now sought-after collector's items.
When he filed a claim with NRA insurance they sent him a check for $400. He refused to accept the check, and filed a complaint with NRA headquarters in VA. To make a long story a bit shorter, I'll just say that he argued with several people at NRA for 4 or 5 months and finally settled for around $800 for his loss, which isn't even half of it's actual value as a collector item in like new condition.
A few months later the Bradenton FL police arrested a thief who had the Colt stashed in his trailer along with several other stolen items. They checked the BATF sales records of the gun dealer and returned the gun to him, and then he returned it to my friend. Needless to say, he hasn't renewed his NRA membership since then and neither have I. When NRA phone solicitors call me trying to get me to rejoin I tell the caller no way Jose.
IMO NRA has turned into a money making racket during LaPierre's presidency, and the most effective major gun owner's org that actually fights for 2nd A rights instead of just begging for money is Gun Owners of America with Larry Pratt as president.