It would be very wrong to impose modern concepts of ethnicity and nationalism too strictly onto the Greek peoples. I don't know how the distinctions between the peoples developed over the long centuries of Antiquity, but certainly in the Classical period they were mostly superficial. The four main peoples tended to share a Greek dialect, an origin story (although often many variants of these existed), and certain religious cults and practices; however, all this usually led to no more than a vague sense of kinship and optional group responsibility. Wars between members of the same group were common (for instance, the rivalry between the Dorian communities of Argos and Sparta, which flared up intermittently for centuries), while inter-group alliances don't seem to have raised any eyebrows.

Ultimately, the four ethnicities were just one of the many different layers of Greek self-identification, nestled between the overall concept of Greekness and the smaller, often overlapping identities of regions, city-states, tribes or demes within states, socio-economic groups, political factions and so on. Few Greeks seem to have specifically self-identified as Dorians, Ionians or the like.

I have never heard of any physical traits being associated with particular Greek peoples. I'd be interested to know where you found that information. They are unlikely to represent a real situation, given that the mythical migratory patterns that gave rise to the distinct peoples of Greece are notoriously difficult to trace archaeologically, and the Ancient Greeks were probably much more closely related and intermingled than they themselves preferred to claim. Stereotypes of course existed - the Ionians of Asia Minor were seen as poor fighters, and the Aeolian Boeotians were mocked as hillbillies - but again, these would not have had much grounding in reality, and exist merely as ideas among other groups hoping to identify their own group by contrasting it with another. Notably, these stereotypes did not follow strictly ethnic lines, referring instead to regional identities.

Follow-up/related: Do we have any idea how prevalent the Classically stereotypical physical traits for each group (e.g. big strapping blond-haired Dorians) actually were in those populations?

Separate question... why do these pertain to the modes of a major scale in western music?