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.

Update: This is no longer current information.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.