My parents would be in relaxed neutral territory, I suppose.
My mom never liked guns, and was always afraid of them (she is still afraid of my guns now, even as I am a police officer)... But she never had a problem with me having toy guns, and never spoke of outlawing guns.
My dad was military at one point in his life. He never really liked guns or hunting (his best friend died in a hunting accident when he was young), and considered them to be tools of the trade for military/police/hunters/etc. My dad was always fine with private gun ownership, though he never owned guns. Much to his credit, he did buy me a BB gun rifle and pellet pistol when I was very young, and taught me about firearms safety (he was big on that). He also let my uncle/grandfather teach me how to shoot, and let me go hunting with some neighbors (family friends) who were avid hunters.
When I was around 15 years old my dad bought me a shotgun (a mossberg 500 I still have), after a few weeks of pleading with him to convince my mom it was okay!
So, I suppose I'd say that my parents were acceptingly neutral: They had no interest in personally owning guns, but they weren't opposed to me learning how to shoot, wanting to shoot, and owning guns.