This term, which refers to beliefs and standards as to what behavior is acceptable or not, is sometimes used in a way that insinuates morality is an exclusive province of religious conservatives. Thus conservative morals, values and beliefs about “the good” are spoken of as “morality” generally.  

While it’s true that conservatives tend to use a narrative that emphasizes morality generally more than liberals do, it’s also true that all people have moral sensibilities on on a host of topics. As a way to open the conversation space, it can be helpful to make transparent what shared values there are with regard any matter in dispute - one acknowledging the possibility (and reality) of contrasting views of “the good” (and bad) held by people with very different worldviews.