Short answer
Yes, keep shallots completely out of reach. They are highly toxic to cats, even in small amounts, and more concentrated than onions. Store them securely in a closed cupboard or pantry your cat cannot access. If your cat ever gets into them, call your vet or the ASPCA Animal Poison Control Center at (888) 426-4435 immediately.
Shallot — Food safety facts
Do not feed · Cats · full breakdown on the linked food page
Allium toxicity — more concentrated than onion. Keep them out of reach.
The full verdict, portion guidance and serving notes are collected on the Shallot food facts page.