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.
You're from Maryland, so I looked that up:
2010 Maryland Code
TRANSPORTATION
TITLE 21 - VEHICLE LAWS - RULES OF THE ROAD
Subtitle 12 - Operation of Bicycles and Play Vehicles
Section 21-1207 - Lamps and other equipment on bicycles and motor scooters.
§ 21-1207. Lamps and other equipment on bicycles and motor scooters.
(a) Lamp and reflector.-
(1) If a bicycle or a motor scooter is used on a highway at any time when, due to insufficient light or unfavorable atmospheric conditions, persons and vehicles on the highway are not clearly discernible at a distance of 1,000 feet, the bicycle or motor scooter shall be equipped:
(i) On the front, with a lamp that emits a white light visible from a distance of at least 500 feet to the front; and
(ii) On the rear, with a red reflector of a type approved by the Administration and visible from all distances from 600 feet to 100 feet to the rear when directly in front of lawful upper beams of head lamps on a motor vehicle.
(2) A bicycle or bicyclist may be equipped with a functioning lamp that acts as a reflector and emits a red light or a flashing amber light visible from a distance of 500 feet to the rear instead of or in addition to the red reflector required by paragraph (1) of this subsection.
(b) Bell.- Subject to subsection (c) of this section, a person may operate a bicycle or a motor scooter that is equipped with a bell or other device capable of giving a signal audible for a distance of at least 100 feet.
(c) Sirens or whistles.- A bicycle or motor scooter may not be equipped with nor may any person use on a bicycle any siren or whistle.
(d) Brake.- Every bicycle and motor scooter shall be equipped with a braking system capable of stopping from a speed of 10 miles per hour within 15 feet on dry, level, clean pavement.
Just like the California code, Maryland doesn't say anything about strobes.
I don't want to waste my time looking at the other 50 states codes, but I would like to know where you found that strobes were illegal.