I’d say most shadiness of the NRA has to do with their lobbying efforts, and especially how closely they are tied to the gun manufacturing industry.
In fact, among hardcore 2nd amendment advocates, there has been a movement to stop supporting the NRA due to corruption, poor management, bloat, and a perception they don’t do enough to support 2nd amendment right, and only further their own existence. [0]
[0] - https://www.reddit.com/r/progun/comments/c3e4rs/hickok45_for...
Then, some time in the '70s or '80s or so, they decided they really wanted to make lots more money, and the way to do that was to radicalize their support base. These days, they not only oppose any and all restrictions on the purchase of firearms (including preventing random people from getting their hands on military hardware, preventing convicted violent felons, domestic abusers, and the mentally ill from buying firearms, etc), but they are actively involved in spreading propaganda to keep their base scared of an Other that they'll need guns to protect them from. This ranges from Democrats coming to take their guns, to immigrants coming to take their jerbs, to brown people coming to take their women.
They foment racism and hatred, specifically in order to ensure that people will keep paying them to protect the only amendment to the Constitution that's truly sacred: the right of every single real (white, straight, cis, Christian, male) American to own whatever guns he wants.