"their conservatism is not what got them banned" also does not refute "only conservatives were banned".
(FWIW, I'm at least as strongly opposed to both sides as they are to each other, although that doesn't really have any bearing on "You are committing the logical fallacy of conflating "only X" versus "all X".". Edit, aside: "existential" qualifier would be "some X", not "only X"; is there a term for "not any non-X"?)
(FWIW, I'm at least as strongly opposed to both sides as they are to each other, although that doesn't really have any bearing on "You are committing the logical fallacy of conflating "only X" versus "all X".". Edit, aside: "existential" qualifier would be "some X", not "only X"; is there a term for "not any non-X"?)