Also, depending on how the bullets get caught at the range (shredded tires vs sand vs steel backstops), they tend to produce a lots of fine lead dust[1].
Also, be aware that most primers usually have some kind of heavy metal in them (lead azide, lead styphnate, mercury fulminate) though there are newer compositions using strontium and tetrazine starting to get traction. [https://en.m.wikipedia.org/wiki/Mercury(II)_fulminate]
Additionally, non-jacketed bullets (common with rim fire, low power pistol, blackpowder, and some other random stuff) will blast lead off the back of the bullets at the muzzle or forcing cone and into the air.
If the area is adequately ventilated it’s not really an issue. Some indoor ranges are not! Sometimes significant amounts of fine particulates can end up at shooting stations from it, or be inhaled.
That said, just wash your hands and don’t hang out in ranges that get Smokey and you’ll be fine. If you’re cleaning up a range with bad ventilation, wear a respirator rated for metal dust.
I’ve done all the high risk activities (including a decent amount of soldering with gasp leaded solder) for over 3 decades, have done that, and have tested ‘non-detectable’ for lead and mercury every time I felt like checking.
I’ve had friends who didn’t that ended up on Chelation therapy. Don’t be like them. They’re miserable.
If you wash your hands with soap and water before sticking them in your mouth after any of these activities, you’ll be fine. If you don’t, I wouldn’t recommend making whatever it was a habit.
If you handled a lot of powdered/pulverized lead powder, and then stick your hands in your mouth and lick your fingers - it could conceivably cause a measurable body burden of lead even if you did it once, maybe. So don’t do that.
"not washing their hands" being the key part. it isn't dangerous to handle diver weights or clean up a shooting range. if the traces aren't cleaned off your hands before touching the face/eyes, eating, smoking cigarettes, etc, the lead will get into the body and cause problems.
[1] - https://youtu.be/QfDoQwIAaXg