Not sure what you meant by strobes, but lights sold in America with a flash pattern, what some will call strobe, is not illegal, if they were illegal the light manufactures would not be able to put that function on the light; like in the UK, flashing lights of any kind, front or rear, is illegal, so lights sold there do have a flash function.
The California code says this:
California Vehicle Code Division 11 Chapter 1 Article 4 Section 21201 (d) covers the requirements for cyclists when riding in darkness. It states:
A bicycle operated during darkness upon a highway, a sidewalk where bicycle operation is not prohibited by the local jurisdiction, or a bikeway, as defined in Section 890.4 of the Streets and Highways Code, shall be equipped with all of the following:
(1) A lamp emitting a white light that, while the bicycle is in motion, illuminates the highway, sidewalk, or bikeway in front of the bicyclist and is visible from a distance of 300 feet in front and from the sides of the bicycle.
(2) A red reflector on the rear that shall be visible from a distance of 500 feet to the rear when directly in front of lawful upper beams of headlamps on a motor vehicle.
(3) A white or yellow reflector on each pedal, shoe, or ankle visible from the front and rear of the bicycle from a distance of 200 feet.
(4) A white or yellow reflector on each side forward of the center of the bicycle, and a white or red reflector on each side to the rear of the center of the bicycle, except that bicycles that are equipped with reflectorized tires on the front and the rear need not be equipped with these side reflectors.
No mention of flashing lights.