Wow, I had never in my life heard of places that don't allow fences till now. I could NEVER buy a home in a place like that. We are currently fencing in our yard for several reasons. We want to keep people out (we've had some door to door solicitors, one who asked for food, plus countless people parking on the street our backyard faces--not our subdivision--just to look at the view of the city, hook up with their bf/gf, or enter my yard like some guy last week), keep our kids in (so they can play in the yard/on the playground while I don't have to worry about them running into the road), plus we have a dog who would love to be free in the yard when the kids are back there (or even alone). I don't want an electric fence at all--while that would likely keep my dog in, it would definitely NOT keep bobcats, mountain lions, javelinas, coyotes, etc. OUT. So my dog would be sitting prey for them. And she's a 71lbs 9 month old puppy, but I still worry that she could be attacked and killed by another animal. Heck, even another dog could attack her! We also have a pool so that needs to be fenced too, not just so others can't get in it, but so that my kids can't get to it even from our own yard. It isn't a law here (we live int he "county" as opposed to the "city" so there isn't a law for that here), but it is just safety common sense.
And we live in a very safe, fairly un-trafficked area. But even with that, there is no way I'd want my kids out in the yard alone knowing they could run into the street at will to chase a ball, or have some weirdo enter my yard and possibly hurt one of my kids, or have my dog run away or be attacked by an animal. Or my kids could even be attacked by an animal!
Anyway, to the OP, I don't know what I'd do if I were you (and I speak from someone who is meeting MUCH opposition from a neighbor regarding our fence right now). If you ask your neighbor, and he says he doesn't like the idea of your fence, well, then what? Will you not put it up? If you won't, then ask away. if you are installing it either way, then you'll just seem like a jerk for putting up the fence he said he hates.