affirmative action: https://www.aclu.org/issues/racial-justice/affirmative-actio...
voter id (are all the other countries that have this violating their citizens' civil rights?): https://www.aclu.org/other/oppose-voter-id-legislation-fact-...
religious liberty (an employer engages in voluntary exchange... not much of a stretch to see it as a violation of rights to force them to pay for something which they consider blasphemous): https://action.aclu.org/secure/your-boss-has-no-business-you...
abortion (Roe v Wade federal overreach vs States' Rights... this and other issues like marijuana laws can be left to the States but "leftists" generally prefer a stronger central government over States as "laboratories of democracy"): https://www.aclu.org/issues/reproductive-freedom/abortion
ACA/"Obamacare": I couldn't find anything about their position on this issue but, if they were only defending civil rights rather than also being a "left-leaning political organization", I think they'd actively oppose forcing people to pay corporations for products they don't want.