Age discrimination in the US only applies if you're discriminating against them for being over 40. This doesn't apply here since they're being rejected for their birthday and not their age.
I still don't think you can discriminate based on something a person has no control over. This person should file a complaint and name the company by name so I know to avoid it.
You absolutely can refuse to hire someone (in the US) for something they have no control of, assuming it's not one of the few protected classes. I could refuse to hire you over height, inability to grow facial hair, etc with zero repercussions.