Ask HN: Are you allowed to discriminate against an H1B holder?

I am a US based software developer on an H1B and was wondering whether employers are allowed to discriminate against H1B holders even though it is relatively simple to transfer the H1B to another firm. I wouldn't even be subject to the cap. There is a relatively small transfer fee but nothing compared to the cost of sponsorship. I've been seeing job postings and responses such as "the company is not open to H1B sponsorship", which I understand because of the high fees involved in sponsorship. But is it illegal to discriminate against people who have already been sponsored and only require a transfer?