Oh, okay, this is... way less dystopian than I thought it was, from the description. If it's entirely voluntary, that's not so bad. Still weird, but evidently you're still able to go with whoever you want, you just get a big nudge towards whoever is genetically compatible to you. As long as you can opt out of having your genetic profile available to the people running this, and they have heavy oversight to ensure that they aren't getting up to shady stuff with the data, it's not a terrible practice.
There's cultural ethics concerns to be had, of course, not to mention the great potential for corruption in the system, but such is always a concern with these sorts of initiatives, and such concerns call for prudence more than anything.
And of course, the idea of incest producing a perfectly healthy child, or even an abnormally healthy one, is far from unusual. They are at higher risk of complications, of course, but a single generation of incest is actually very unlikely to result in issues. The main problem with incest is that this risk compounds. So one generation of incest seems fine, the children are healthy and happy. But then a few more generations go by, and suddenly you've got frequent miscarriages, awful conditions of the body and mind, and the whole bloodline is at the brink of collapse.
But in modern times we know the risks, more or less, so there's little risk of such things happening. Indeed, we are likely more incest averse than necessary, as an overreaction of sorts to the overabundance of it in earlier times.