The once-common software development term "master branch" is now considered problematic due to the association of the word "master" with slavery. However, I am not aware of any criticism of the term "master's degree." What is the difference? Is it because master's degrees have existed for centuries, compared to just a few decades for master branches?
When "master" is used in computing contexts, it refers to an entity that has primary control over data that is replicated in other entities (as in master branches or master database servers), or controls other devices (as in "bus master"). This is based on a metaphor of the way slave masters control slaves, which is the reason it's considered problematic. While users of the term may not deliberately intend to refer to slavery, the metaphor may be considered to minimize the horror of the original activity.
I've been informed in comments that "master branch" wasn't intended to refer to control over other branches, but to be more like "master copy", meaning the original copy. Despite this intent, I think it has become tainted by association with all the other uses of "master" in computing that do use the master/slave analogy. People who see the use don't know what the coiner's intent was, they just view it in the context of their experience as computer programmers, and that has this negative connotation.
(In contrast, there are no benign metaphors based on "holocaust" or "concentration camp". If you call someone a Nazi or fascist, you're intending to evoke how evil these people were, and invite a comparison.)
But in the phrase "master's degree", the word "master" doesn't refer to one person controlling another. It refers to the definition that means being an expert in an activity or field of study. Another uses of this meaning is "chess master" -- they don't control other players, they're just very good players.
There's obviously an etymological relationship. When you become a master of an activity, you're in control of the objects and processes that performing it involves. But the pieces on a chessboard are not considered to have autonomy that is being violated, the way a slave's human rights are, so the two senses are considered sufficiently different that we don't find much difficulty with the second use. It doesn't bring the master/slave relationship to mind.