Bran having brown eyes is far easier to overlook than two brothers of clearly different ethnicity.
No, it's not. People don't have their ethnicity written on their foreheads. You're only saying that because you know who both actors are. Ethnicity is are a social construct and not a biological or genetic one.
It's actually perfectly possible for two full siblings to look very different in terms of
skin color, hair color, eye color, features etc. (not that this is really the case here, apart from maybe skin, and not to a huge extent). That's how genetics work. Even laymen know that it's not that unusual for one child to take more after one parent and the other more after the other.
It is actually possible for two parents to carry separate "recessive" genes that require the other specific allele in some way to exhibit. Punnett squares aren't nearly the whole story. While it may be theoretically possible for two children of "multi-ethnic" parents to take dramatically after one and the other original ethnicities, it is far less plausible.
The problem is that in this case, one of the parents would have to carry a DOMINANT gene for brown eyes and still somehow have blue eyes. That's not possible. I think I may have heard that it could perhaps happen if there is a rare mutation of the gene, but that's all.
The Baratheons typically being dark of hair fits right in with other prominent families in Westeros. Lannisters typically have golden hair and green eyes. Tullys typically have red hair and blue eyes. Starks typically have dark hair and grey eyes. Targaryens typically have silver-gold hair and violet eyes. There are some exceptions, of course, but the implication is that members of these families routinely develop these particular traits. It's a fantasy world, so I don't find it particularly odd.
Yeah, families retaining their physical characteristics for centuries is pretty unlikely (though when it comes to the Targaryens and, judging by the Stark family tree from the leaked pages from the World of Ice and Fire book, it's not that surprising, since there was a great deal of inbreeding involved). But still, we get no other examples of a family where one trait was always carried over in every child in the male line.
For instance, in the book, the only Stark children who hae the Stark look are Arya and Jon, the other four all have the Tully auburn hair and blue eyes. Baelor Breakspear (son of Daeron the Good) and his sons had dark hair like Baelor's Martell mother, while his brother Maekar and at least two of his sons had the Targaryen look. Rhaegar's and Elia's daughter Rhaenys had dark hair while their son Aegon had silver hair. And as we find out in the WOIAF excerpt, the "Baratheon" look (and sigil, and words) is actually the
Durrandon look - that's how king Argillac looked like, and presumably his daughter Argalia, who married Orys Baratheon (of Valyrian descent and probably bastard half-brother of Aegon, Rhaenys and Visenya). So, it's not like there's something special about the male line, genetics-wise; therefore, the last name should not always be reflective of the look.