McMurdo has starlink. South Pole doesn't, but not due to technical reasons from starlink's side. From what I understand when they tested at Pole they noticed interference with some of the science experiments, its possible they will engineer around that at some point but for now starlink is a low priority compared to ensuring the science goes on.
I forget the exact distance, but its something like 5 miles from pole that they ask groups traversing to turn off their starlink.
that is to say, the starlink terminals radiating EM sufficient to mess with the sensitive sensors at the south pole, which is fascinating since they're supposed to have passed compliance testing that they're not doing too much of that. but the south pole has a different definition of too much, it seems. fascinating!