While Hilde does show interracial breeding, its worth remembering that that interracial breeding was considered scandalous. Her mother wasn't thrown on to the streets because Hilde was a bastard, but because she was a mixed race bastard. That was the scandal.
As a result I suspect there is a degree of social stigma. Certainly we see nothing to suggest that such pairings are common.
As for the Dragoons:
the fact that Ishgard's populous at all had draconic essence in their veins was a secret enforced by the Holy See. Certainly the Dragoons themselves showed no knowledge of it. Estinien was shocked at the truth. Its also worth noting that the WoL when they gain new abilities literally have it say "the dragon within stirs" or some such. I'm not sure that directly has anything to do with Hydaelyn.
Regardless I don't think we have a definitive answer yet.