My father started me at two-and-a-half. Grampa's yard, M1 carbine and .22 revolver, Dad held the gun or my hands to make sure of the safety. I can actually remember it, and date the memories, because that's the summer Dad turned the M1 in for a G3 (gov't property).
I don't remember when I first visited a range, but probably before my 4th birthday. That would have been a club range where the other shooters knew Dad, I guess that makes it different from a commercial range with strangers. I think the other shooters found it amusing to watch a four year old demonstrate safe gun handling. But I'm quite sure my Dad or someone he trusted kept a close eye on me at all times.
Full auto? I think I was 8 or 10 before I got to shoot a gun that was designed for it. But I'm probably one of the few to have experienced a P08 Luger go "full auto" on me (malfunction) - at the age of 3.
Seriously, a responsible four year old shouldn't be a problem, but it does of course help a lot if the father is responsible as well. Children are different, parents are different - and shooting ranges are different.
I think it is better for a child to learn safe gun handling at the earliest possible age, than it is to "learn" from Hollyweird and teenage friends...