It's not much of a restriction, considering that you pretty much fill out your name and address, and send in whatever the yearly dues were back then.
The rifles were intended to be used by civilians to hone their rifle skills engaging in competitive marksmanship events, most of which were administered by the NRA. Hence the connection with the NRA.
NRA membership is no longer required. The qualifications aren't really very stringent. I'm already qualified without even trying. See below.
And you're arguing a strawman. Nobody said there were no purchase restrictions. That's where you went when your disbelief that guns were sold at all by the government to civilians was proven to be in error.
Read all of the requirements toward obtaining parts, ammo and other CMP Sales items, including eligibility and local shipping information.
thecmp.org