Theoretically, yes. However, the ACLU has historically been perceived (especially by the right-wing) as a left-wing organization, since it stood for things like racial equality, religious equality, and most importantly the end to (mostly anti-Communist) restrictions on political expression.
Hence the attacks on Dukakis for being a member of the ACLU during his election campaign, and his joking self-labeling as a "card-carrying member of the ACLU" (in reference to McCarthy's references to "card-carrying Communists").
EDIT: And for yet more historical background - it was originally founded (as the Civil Liberties Bureau) to defend anti-war speech and conscientious objection during World War I, which were mostly left-wing and far-left-wing phenomena. Post-war, in addition to serving as an ethnically-neutral counterpart to ethnic civil-liberties organizations such as the ADL (Jewish) and the NAACP (African-American), it spent a lot of time defending free political speech. And the free political speech that was most under attack through its seminal period in the 1920s was labor organizing and socialist politics. (Because of the phenomenon of white-supremacist Southern Democrats, minority-rights issues did not necessarily line up with party politics, but they were indeed perceived as left-right issues in the sense that racial equality was considered a far-left position.)