What is the status of a cohen who intermarries? He would not be able to eat Trumah, but does he continue to receive the first aliyah, and can he duchan (assuming he observes all other mitzvot)?
A Kohein who marries a woman who is forbidden to him because he is a Kohein or a Kohein who defiles himself with corpse-related impurity does not bless the people and does not get any of the special privileges of being a Kohein (eg. called to the Torah first) until he stops doing the forbidden action and accepts to never do it again. (Shulchan Aruch OC 128:40-41)