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Update: This is no longer current information. See the answer by DavidSupportsMonica regarding summer 2022 reservation requirements.
This has now changed as of summer 2021, but only if you're truly driving straight through by the most direct route without any stops at all. According to the FAQ:
Do I need a day-use reservation if I am just driving through the park?
You can drive through the park to reach a destination on the other side of the park without a reservation. The entrance station ranger will provide a time-stamped permit valid for the time needed to travel from entrance to entrance. You must drive the most direct route to exit the park; stopping is prohibited. Violating park regulations can result in a fine of up to $5,000 and/or six months in jail.
The park entrance fee still applies and provides access to visit Hetch Hetchy during open hours when it's not full.
Upvote:4
UPDATE Spring 2022:
From May 20 to September 30, 2022, the Tioga Road will again require an advance reservation in order to enter the Park between 6:00 a.m. and 4:00 p.m. The new requirement is detailed on this National Park Service page.
Reservations cost 2.00 (this fee is in addition to the regular Park entry fee) and are valid for three consecutive days, including the day of arrival.
Upvote:5
Yes, you will need a day-use reservation to drive through the Park.
The NPS's Yosemite page contains this FAQ:
I am just driving through the park and not planning to recreate. Do I need a day-use reservation? How can you limit access to a state highway?
Yes, you still need a day-use reservation. Tioga Road, which connects with Highway 120 at the park boundaries near Big Oak Flat and Tioga Pass, is not and has never been a state highway. Originally a private mining road, private citizens purchased the road and donated it to the National Park Service, which has improved and maintained the road ever since. The National Park Service is solely responsible for providing road maintenance, as well as law enforcement and emergency services, along all roads within Yosemite National Park.