Especially children with intellectual disabilities can't seek out the outside world on their own. I don't know how far the parent should broaden their hobbies and world.

An important question, with no single right balance. In common: new experiences broaden the world, but deepening a secure "favorite thing" also has value. Using the child's reactions (enjoying, feeling secure, tiring, disliking) as clues, trying in small amounts is the basic approach. What the family decides: whether to weight broadening the range of experience or respecting the child's likes and security is your choice. A guide: "is the child enjoying it?" "is the newness a burden?" "can you broaden it via a like as the doorway?" Broadening and protecting are both for the child. Watching the child's signs, going back and forth is fine.