Eileen comes from a place where doctors are often the people send out to murder infected civilians (often calling it a "preventative cure") so she'll be pretty wary around Stein. His offers of dissection really don't help.

After is seems clear that he's not going to be shoving a blade through anyone's neck for coughing too much, though, she'll warm up to him. He still can't dissect her, though. Not even after she's dead - and she'll make sure the likes of Booker and Toriel know that so that they won't let it happen.