Short answer
Yes, gooseberries are safe for cats, but it's still wise to store them securely. Keep them in the refrigerator or inside a sealed, cat-proof container rather than leaving them in a bowl on the counter. Training a solid 'leave it' command is also helpful for preventing future curiosity. If your cat does sneak a few ripe berries, just watch for mild stomach upset from the acidity and call your own vet if anything seems off.
Gooseberry — Food safety facts
Safe to share · Cats · full breakdown on the linked food page
A few ripe berries are safe. Watch for stomach upset from the acidity.
The full verdict, portion guidance and serving notes are collected on the Gooseberry food facts page.