Black and Hispanic people do face more active discrimination. That has to do more with outward appearance and last names.
Vets on the other hand are an example of a lop-sided outcome. It was discovered a while back that most vets often went into blue collar professions and didn't really climb that many ladders. They instituted a rule where campaign badge holders and disabled vets must have their resumes reviewed first. Working on the west coast I can attest it's rare to see vets at all. I've met more vets from non-US military in the tech world than I have from my own country (not complaining, but worth noting). There's definitely a small contingent of people who would put their political disposition into hiring if they saw a candidate was a vet, but military are coached to chop their military experience from their resume once they have a stack of experience to avoid this.
All that to say, if I were OP I would not be okay with what you proposed just on a facade basis. If it incorporated class distinctions I might agree.