My wife has no California ID and none of the utility bills are on her name. Can she bring car insurance or bank statements as proof of California residency?

Because of the pandemic. I would suggest her getting a California ID. It's up to you, but it depends on which theme parks your going to. I hope this helps.

We were a party of 8 and only the person who purchased the ticket was asked for an ID. Maybe give them a call?

They do require an ID to be present. You can use a passport as well. But bills or bank card won't be enough

I think it will be ok. No one checked our ID's there yesterday (05/03/2021), but it can always be subject to change.