[Coda]

Technically they're allowed to ask for one -- in and of itself, the request isn't illegal.

That said, there are a lot of reasons why you're permitted to politely refuse. It is illegal to make hiring decisions based on race, ethnicity, religion, disability, gender, or age, and you've got a federally-mandated right to refuse to answer questions about those. It IS illegal to DIRECTLY ask about any of these, but there are a lot of questions that would IMPLY these, and you're not required to answer the questions if it would.

And since a photograph could reveal ALL of those, you are within your rights to make an image file saying that you decline to provide a photograph under your rights granted by federal non-discrimination law and upload that in place of a photo.