Our cats get out...I've tried everything to keep them indoors because we live in a suburb of a large city, but it's a no-go. I don't have my hens yet but when I get them I know I'll have to be very very careful when they're young, because my older cat would go for them for sure. The largest animal he's killed, though, was a blackbird, so I suppose that if I get Sussex or Delawares they should be ok when they're full grown. I can't see Monster taking on anything that size.
As to the neighbors...I really really hope they're ok with our cats outside. I've never minded a roaming cat but I have issues with roaming dogs. They're just different in my mind, and a dog can cause a lot more trouble. Both of my cats are fixed, so they're not out chasing queens in heat, and for the most part they don't go too far. I have had my older cat's collar returned a couple of times after he lost it near someone's house, and once in their garage. I want to get a tag for it that says 'I'm really really sorry my cat is roaming in your yard.' on the back, but I don't think it would do much. I hope the neighbors will come talk to me if they have issues with my animals, that's for sure, so that hopefully I can come up with a solution to the problem.
They have a cat door to get back in, but not out, so they're not trapped outside for extended periods, though Monster does occasionally get stuck up on the roof somehow and holler for assistance.
Back to the original question, though...I think any bantam is fair game for a cat if it or the cat is roaming free, but the larger birds have got to be too big to handle.