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In Bumblebee (2018), Sally gifts her daughter a helmet:

Sally: So, I keep hearing about people on mopeds getting run over and their brains smashed in. You got to wear this from now on. I don't care if it's not the law. It's our law.

Why did she say wearing helmets isn’t included in the law while driving mopeds?

The majority of the film is set in 1987 California and the state had no motorcycle helmet law until 1st January 1992.

To evaluate helmet use in California before and after the introduction of an unrestricted helmet use law on January 1, 1992, observations of motorcycles and their riders were made at 60 locations in seven California counties, twice before and four times after the law was introduced. Helmet use increased from about 50% in 1991 to more than 99% throughout 1992. Compliance was achieved despite variations in helmet use by motorcycle design and road type. Seven percent of riders used nonstandard helmets after the law.

_{—"Compliance with the 1992 California motorcycle helmet use law.", J F Kraus, C Peek, and A Williams, NCBI}

Because it's not the law.

Although many states have some laws requiring wearing of helmets on motorcyles / modes, this is not universally the case.

Motorcycle helmet laws vary widely among the states and have changed a lot in the past half a century. Currently (April 2019), 19 states and the District of Columbia have laws requiring all riders (operators and passengers) to wear a helmet, known as universal helmet laws. Laws requiring only some motorcyclists to wear a helmet are in place in 28 states. There is no motorcycle helmet use law in three states (Illinois, Iowa and New Hampshire).

In the past, many more states had universal helmet laws, thanks to pressure from the federal government. In 1967, states were required to enact helmet use laws in order to qualify for certain federal safety programs and highway construction funds. The federal incentive worked. By the early 1970s, almost all the states had universal motorcycle helmet laws. However, in 1976, states successfully lobbied Congress to stop the Department of Transportation from assessing financial penalties on states without helmet laws.

Low-power cycle is a generic term used by IIHS to cover motor-driven cycles, mopeds, scooters, and various other 2-wheeled cycles excluded from the motorcycle definition. While state laws vary, a cycle with an engine displacement of 50 cubic centimeters or less, brake horsepower of 2 or less, and top speeds of 30 mph or less typically is considered an low-power cycle. Twenty-three states have motorcycle helmet laws that cover all low-power cycles. Twenty-four states and the District of Columbia have laws that cover some low-power cycles

^Source

According to: Helmets in the USA

States began to adopt laws on wearing helmets for bicycle riding in
1987

Moped are technically classified as "Motorized bicycles".

The film Bumblebee is also set in 1987.

Hence, that law might not have been in effect in that area at the time.