I was living out the Gulf in the late 90s. Theoretically, I had to take a bunch of medical tests - including HIV screening - to get a Bahrain residency visa. I was never asked to do it, nor would I have a agreed. I asked a friend about it, he laughed and said "that's for the Indian, Pakistani, Thai and Filipina guest workers, not us".
If the DNA testing thing sees the light of day, it will probably be along the same lines. Only the unwashed (literally sometimes) will have to do it.