Goodman, Jackson, and Fricker are non-contextualist. However,
the mainstream epistemology is contextualist.
The adverb "however" is the best-fitting word as it modifies the entire clause, conveying that the entire clause in someway contrasts or contradicts the information that the prior clause or sentence conveys.
Incidentally, "on the other hand" does fit there. You could aptly say "on the other hand" instead of "however" because Goodman, Jackson, and Fricker being non-contexualist is the opposite of the mainstream epistemology, which is contextualist.
Both "whereas" and "while" cannot be used as they are subordinating conjunctions. Using those words to introduce the ensuing clause turns it into a subordinate clause, a subordinate clause without a main clause, thus a fragment rather than a complete sentence.
Also, were the second sentence instead a subordinate clause, meaning the period beforehand would be changed to a comma to make it part of the prior sentence, you would not follow it with a comma. To be clear, were you to use either "whereas" or "while," the two sentences would have to be combined into one sentence: "Goodman, Jackson, and Fricker are non-contextualist, whereas/while the mainstream epistemology is contextualist."