It's an actual requirement to give your personal information to gun stores when buying a gun so they can do a background check. They are prohibited by law from using that info for purposes like marketing, but they still have to collect and store it, and I'm sure all of them don't have great privacy policies. Even morons in the 1990s understood that.
This isn't about the data gathered on Form 4473s for the purposes of running background checks. This is about people filling out the warranty cards that came with the guns.
I've always kind of assumed the primary purpose of these is building customer lists. Were they at any point actually important in seeking warranty reimbursement or repair? I suspect that at almost 40 I reached adulthood about the time that the internet shifted the way a lot of old customer service systems worked.
They are only for collecting user data. Firearm manus tend to either cover everything aside from user modifications/damage, no questions asked, or cover nothing.
4473s are a different, far worse, form of privacy invasion. Ostensibly used for background checks, kept forever in order for the ATF to do fishing expeditions.