Turo Insurance Agency works with Liberty Mutual Insurance to cover hosted vehicles. For hosts, they claim to offer $1 million in liability, but their physical damage protection is a separate thing. That's where you choose your level of protection and cough up a fee with the promise of "contractual reimbursement" if your car is affected during the trip.
It's up to you which level of insurance you get — you'll want to balance it with your vehicle's projected value — but I recommend taking the high road whenever possible.