Used to be they could ask about anything they wanted, and they did. The majors also gave you an astronaut physical.

Today it's a little complicated since state laws can vary but *in general* airlines have evolved their practice to one or two approaches, both of which seem to be legal...

1. Look at, and photocopy, your FAA 1C.
2. Have a staff (or contract) AME administer an FAA 1C exam to verify that you meet the standards. They're entitled to do this since FAA exams are conducted not by the FAA itself but by third party designees (AMEs) so they have no guarantee of consistency on the application of the standards.

What you're describing might be associated with #2?

The employer in question apparently thinks it's legal to ask. If it's a big airline, they almost certainly know what they're doing. If it's smaller shop, maybe they're coloring outside the lines?

You'd probably need an aviation attorney, with experience in that state, to give you a reliable answer.