Another thing to take into consideration with the rulings is the affect a child will have in the game. I mean if said female is a PC well there goes that char you ever seen a pregnant women walk up a hill? Now imagine that same women lugging around a 150lbs pack marching for 8hours a day and all other adventure based things. Now think about the male (im assuming he is the PC) will he give up his career as an intrepid adventurer to get a steady job with less risk of death? just my 2p
Didn't native American women use to pretty much walk along with the tribe all over the place and then just excuse herself for a bit when the due date finally rolled around, only to catch up virtually immediately afterward?
Biologically it's not that mammal vs hard egg would be a big issue (the way that early mammal cells divide and structure themselves is actually exactly the same thing as reptiles or birds, but it looks funky when it's not resting on a big yolk.) The two issues that actually stop this kind of thing are if the genes are so different that combining them just makes a tortured mess worse than you'd find in a Cronenberg flick, or if the immune system of the mother picks up on some really foreign/out of balance stuff and decides this lump isn't a viable baby. I'd rule the second case in the real world but when you've got Tieflings viable through multiple generations and minotaurs running around I don't think a dragonborn mix would be the biggest deviation from a humanoid's body plan.
But back to the table, I agree that what matters is what kind of story you can tell.
As many have stated before, you can make whatever ruling you want at your table. There is no clear ruling on your question. At my table, I would allow it if I wanted it to happen (i.e. if it furthered the story in some way and didn't bugger up the rest of the world). If I were to make a ruling based on current, and prior, edition rules...I would say no.
[Disclaimer: There has been tons of material published over the years from a variety of sources, but I am focusing on the core-game rules/mechanics]
Assuming that interspecies breeding leads to 'half' races, the only ones we see with any regularity are half-elves and half-orcs. We also see half-ogres and half-dragons on occasion. The first two imply that elves, humans, and orcs can interbreed. Apparently ogres can also breed with something, presumably humans I guess. Dragons can shape shift in order to breed, so they differ from the other groups.
We have no half dwarfs, half gnomes, etc. I would posit that these races are much closer to humans than are dragonborn (biologically). If they can't interbreed, I can't see dragonborn being able to interbreed.
I am sure that somewhere in the D&D publishing history we could find a half version of almost every major race. So an argument could also be made to allow it, based on prior rules. I just don't think it is as strong of an argument.
The Dark Sun setting seems prominent enough to shrink the list before we do any deep dives.