The truth is, while they may not show any signs of being wary of me, I feel the need to assuage any concerns they might have, as if the fault is somehow mine, just by being male and present.
I'm not sure I've ever really examined it deeply before. it's eye-opening, to say the least.
Even in gathering of my closest friends, where we share implicit trust that every parent is looking out for all our children, I still take great care to be aware of where I'm placing myself relative to a parent and his or her child. If I find myself blocking some parents' view of his or her child, I move. I (obviously) don't do this because I think they'll suspect me of some malfeasance, but simply because I know they'll feel ever-so-slightly more comfortable being able to see their kid.
Playgrounds are the modern analog to a watering hole: an ad hoc "tribe" forms around them, and by making it clear that your kids are at the playground, you're saying, "I'm not an outsider, I'm a member of this tribe, you can feel comfortable with me." Women do exactly the same thing, it just manifests differently; usually in the form of smalltalk and mini-conversations with other parents.