I suspect that its a combination of some superset of the following factors:
- Intermarriage and conversion bringing in genetic material from the host population.
- Diet affecting people's hardiness, skin color, etc.
- Standard of dental care affecting people's facial structure and whether they like to open their mouths.
- Environmental factors, including sun exposure, which could affect skin color as well as things like hair loss.
- Cultural norms for facial expressions and body language. I suspect that people from Moscow hold their faces like other Muscovites and differently, in a subtle way, from people from Cleveland or Singapore.
As a demonstration of the importance of my four proposed non-hereditary factors, I submit that Ashkenazic Jews who grew up in Israel look subtly but noticeably different from those who grew up in the US, even if they came from the same family origins, going back just a generation or two.
Another example: There's a guy I work with who was born in India. On his employee ID photo, which is from a few years ago, he looks incredibly more Indian than he does now, almost like a different person. I think part of it is that he's put on a little weight , but there's something harder to put my finger on that I'll bet is an American attitude's effect on how he holds his face. I saw a photo in his cubicle that was probably taken between his ID and now, and his "Indianness" seems in between to me.