I think the interest is potentially there in each young person, but social/political movements have been active for a long time and joining those "causes" is still popular. Kids (and their parents) are kept in the dark about firearms, or the firearms are demonized as being "the problem". The opposite - pushing for more outdoors activities, hunting, and gun rights is not quite as celebrated in the news these days.
People brag about being vegetarian, gluten free, kale-smoothie drinkers.
As the agricultural scene becomes less celebrated/desirable in pop culture it makes sense that what is fashionable to do as far as hobbies go would change. Any main stream Prime Time shows about loving families hunting/fishing/shooting together being responsible and making good choices? Wouldn't make the cut. The anti-hero is still popular in movies - the man who is rude, law breaking, perhaps murderous, but is still the "good guy" How popular is it to be safe and follow rules? - that, I think is not new.
As far as safety/responsibility, it's not just with firearms but popular culture tends to say it's the arrow not the indian so *everything is more restrictive. Or "safe". That way less are sued and even the most un-trustworthy child won't have the chance to do himself/herself harm. Until they are not children anymore.
There's nothing intrinsically noble about the shooting sports. But there is a lot that can be learned, experienced, and gained through participating - just as there would be for any sport or discipline. And there's some good folk involved.
Strangely, although most boys have been exposed to firearms in their video games, I don't see every young male seeking to learn to shoot when they come of age. Perhaps the game stays a game in their mind, which may be also a way to keep some with extreme violence from affecting them as well. So far every young person (mostly post graduate age) I've taken shooting has liked it, but just didn't have the uncle/dad/grandpa who taught them to shoot on a family farm. Families are physically spreading apart too, and there's only so much you can do by video phone. Also different cultures/nationalities of course be less likely to have a family background in firearms.