I have 2 kids. I started teaching my daughter at age 5 how to shoot, but started teaching her about guns at age 4.
My son started learning about guns at age 5 and learned (still learning) how to shoot at age 6. He wasn't ready to follow instructions as young as my daughter. My daughter has no interest in playing with toy guns, and the toy guns we have for my son are used as learning tools, not toys. (Finger off the trigger, don't point it at anything you don't intend to shoot, etc).
I started both kids with simple gun safety rules and handling. They had to repeat the guns rules, show safe handling and then we started off with a small BB gun shooting at balloons. My daughter now 9 years old, is shooting at 100 yards keeping about 50% of her shots in the black. My son (7 years old) is shooting a Cricket at 25 yards and is keeping most in the black with about 1 out of 15 in the X ring.
I know many others here let their kids play with toy guns, and many here did play with them as kids. Most of us turned out just fine.