Your first fact is only partially correct. It was founded primarily to help increase marksmanship with a rifle since so many people were such bad shots. During which they held practice, safety and competition events. So it was not strictly a sport hunting organization. https://en.wikipedia.org/wiki/Nation...le_Association " Founded to advance rifle marksmanship, the modern NRA continues to teach firearm competency and safety."
Your second fact is not correct. There has never been a strong movement in this country which passed thru congress to ban all firearms ownership by private citizens. In over 200 years. :P In the 1930's the FBI proposed that all firearms held by private citizens should be registered. Yet dropped the proposal shortly afterwards because it was not realistically enforceable. You are correct that today the NRA and the GOP have been strong supporters of the right of the citizens to keep and bear arms.
Guns are not going to be a nation wide ban here in the US. You can wish, pray and dream it will be, but the odds are strongly against you. More gun control is possible however. Which is why the NRA is a watch dog for those who feel the right to keep and bear arms shall not be infringed.