ALWAYS!!! When we taught our kids how to shoot (starting at age 5 for those who wanted to) we supervised everything and just taught very basic shooting skills and safety points (barrel ALWAYS at target and finger OFF trigger until read to fire) and let everything develop along side their experiences! Our middle child didn't want to shoot until he was 8 y/o...but then took to it like he'd been doing it his entire (albeit 'short') life! In the beginning, I sat next to them at the shooting table and was ready to assist them with any issues should they arise!You are a much better parent before you have kids.
Here we are 11+ years later...and our kids all know the safety rules, how to practice safe gun handling, and why we don't load a magazine into a gun or chamber a round until they're at the mark and ready to shoot...and, most importantly, we all practice gun safety the same way with the same steps, every time...consistently!
Kids can handle a lot of different things...but please keep it age-appropriate and allow them to have a say in what they're comfortable with and what they're not...it's important to them!