American curl breed kittens and cats are indoor cats.
This breed is highly recommended as a city cat and pet for children or grown-ups of any age.
They do not mind indoors. Actually they do not bother to go outside and if they happen to be outside I have not seen one taking any notice of birds or insects other than stepping out of the way.  They are not afraid at all as they had no hunting in mind, they are just polite.
Here is a photo of a kitten I sold few years ago. Very happy in a good home.  The kittens play non stop but they do not play rough in a way that they would knock down and break a vase or something.

Jackie adopted this tortie-point girl photo below.  The girl could not go to a better home, thank you Jackie.

This is what she( the cat girl) thinks of an insect.

awww cute.  Let it go the family is waiting.

These are kittens from our old lines.  The queens have retired from breeding.