That really surprises me--if they stipulated anything you'd think it'd be that the cats should stay indoors.
We keep ours inside. It wasn't my original intention, but I've read so much about cats getting lost, hurt, killed, etc, that when the time came I just didn't want to let them out. Hester is curious about the outdoors, so sometimes I take her out on a lead, but Hugo has no interest in leaving the flat. I get the sense that a lot of people in the UK feel it's cruel to confine cats, but I think the dangers of them going out are just too dangerous. Especially when I read things like those seven black cats that went missing in Yorkshire. If I suspected someone had captured Hester and was doing cruel things to her because she's a black cat I would go out of my mind with worry.
If I didn't rent, I'd build a catio, so they could go outside and still be safe. Is that a possibility where you live? That would probably satisfy the shelters.