Well, they aren't "allowed" to be neutral anymore than anyone else. They just happen to have had things going for them that made it so people didn't need to invade.
Fixed your post.
Generally speaking you don't "need" to invade anyone unless you feel they pose some sort of imminent threat that only invasion can stop, otherwise you're invading because you want to.
Not if you're a mad "realist". In that case, the chance that anyone else might otherwise invade before you do is quite sufficient to make an invasion necessary. (see Norway, WW II. Also, Greece, WW II.) Besides that, there's the issue of getting from a country what you want from it, without an invasion - see Sweden as well as Switzerland in WW II. It's not as if anybody, not even the derangedest dictator, invades countries just because he can.