Yes, even if you have an America the Beautiful National Parks Pass, you still need to pay for parking at Muir Woods.
Your pass covers the per-person entrance fee for you and up to three additional adults, but it does not include parking. Parking reservations must be booked separately at www.gomuirwoods.com in advance, as parking is not sold on-site.
If you are being dropped off (e.g., by taxi, rideshare, or private vehicle), you do not need a parking reservation—just bring your pass to the Visitor Center for entry.