Well to be honest I'm personally not all that concerned with the kids show part (liking stuff like Muppets is actually somewhat trendy), the real reason I don't really want people to know is the other fans. This isn't the case for all fans of course, but I find the really hardcore bronies really annoying. Like they have a pony avatar, pony nickname, pony signature, which is alright by itself, but then you couple it with the fact that they only talk about pony things and use pony grammar like "everypony"- it get's really obnoxious. This would be the case for anything like religion, or heavy metal, or sports teams. But with MLP fans in particular you see it so much and to such a great extent.
On another forum I go on there's like ten people who all have pony avatars and for a while they would post pony shit constantly until moderators stepped (the moderators that weren't part of this group, that is). I mean, I really enjoy the show, I even enjoy the culture with all the memes and fanworks. Again, I know these aren't all of the fans, but there are so many of them exclaiming their love so loudly in the most obnoxious way that it's like "We get that you like ponies. In face I like ponies too. That's cool but seriously we get it. Don't you have other interests?"
That is, speaking in the context of the theoretical case where I also liked ponies.