Anyhoo, if it is likely that two genetically identical populations may have significantly different musculoskeletal development according to their respective environments, could this have implications for fossil-based taxonomy?
This is not inheritance of acquired characteristics because it doesn't occur over generations. This is called plasticity.
Sun tans would be an example of plasticity. Any person other than a complete albino will respond to sunlight by having a darker skin. This is as true for Negroes as it is for Caucasians. The skin responds to the ultraviolet and light by secreting more melanin. The tan has little to do with primary changes in the DNA structure.
The condition of having more melanin because of extra sunshine is referred to as a tan. The tan involves changes in the RNA and protein of the skin cell. The ability to develop a tan is a type of plasticity since the development isn't associated with the primary structure of DNA.
Tans are not hereditary because the DNA structure in the gametes are not affected by the melanin on the skin. A family of pale skinned people who decide to get tans will have pale skinned offspring.
Sunlight can affect the DNA structure in the skin cells. The effect of sunlight on the DNA of individual skin cells is random. For instance, sunlight may destroy the DNA. The skin cell will then die. Sunlight can cause skin cancer. Before modern medicine, acquisition of skin cancer generally killed the organism. Sunlight can affect the DNA of a skin cell by making the cell secrete less melanin. Sunlight can also affect DNA of a skin cell by making the cell secrete more melanin.
People are born with certain complexions do to the genes. The specific structure of DNA is associated with maybe four pairs of genes with about two possible alleles each. Each combination of alleles is associated with a range of potential complexions. This combination is characterizes the populations of people.
Sunshine can change the primary DNA structure in a skin cell. However, this change isn't inherited because it doesn't affect the gametes. In order for a mutation in a skin cell to affect the gametes, there would have to be a high quality communication channel between skin and gonads.
A pale person can roast himself for hours in the sun. His skin could turn dark black due to melanin. A skin cell could even mutate, forming a different DNA sequence at random. There is no way that the gametes in the gonads can change due to the sun. So that person will have children whose genomes are a mixture of genes from that person and the mate.
Skin cancer is caused by a random mutation in the skin. It doesn't directly pass down to the gamete cells. However, skin cancer does contribute to evolution. A person who got skin cancer general in the good old days would die with few exceptions. So they had less children. However, people with less melanin had a better chance of surviving. So in sunny climates, people with the right combination of genes had a better chance of surviving.
There is a trade off. If a person has lots of melanin, then he can't make much vitamin D using sunlight. So people inside northern Europe far from the sea may have suffered rickets from the lack of vitamin D. So the inland Europeans evolved had pale skin. However, people who lived close to the sea can get lots of vitamin from fish. So maybe coast Asians and aboriginal Americans thousands of years ago didn't need sunlight for their vitamin D. However, their was enough sunlight to create a problem with skin cancer. So the balance of risk went against pale skinned people near shore.
Eskimos (e.g., Inuits) get plenty sunshine during the summer. During that time, skin cancer is a risk. They get very little sunshine during the winter. Not only is the sun low in the sky, but their winter cloths are very thick. However, much of their traditional diet at this time comes from cold water fish. Cold water fish have lots of vitamin D. So Eskimos don't need sunshine at any time. Better to be dark skinned so as to avoid skin cancer during the summer. So natural selection doesn't favor pale Eskimos.
I think the skin problem was more or less resolved when those four pairs of genes were discovered. There has been no mechanism discovered by which the condition of the skin affects the structure of those genes in a gamete.
I don't think the fossil record tells you which changes occurred due to plasticity and which due to genetics. This is why there was still a question of Lamark versus Darwin for a long time. For the most part, the question was resolved in favor of Darwin.
Pay attention to the epigenetic research. Someone may find a Lamarkian modification of skin color, yet. No one has found any so far.