The phrase "conscience issue" refers to a problem or situation that has to do with a person's personal moral beliefs or values. It means that they have to make a decision based on what they feel is right or wrong according to their own conscience.
Sentences with «conscience issue»
That's the beauty of free votes on conscience issues, which our party has always respected. (conservativehome.blogs.com)
Since the introduction of proportional representation in 1996, divisions which require all members in the chamber to vote by taking sides (termed a personal vote) are rarely used, except for conscience issues. (en.wikipedia.org)
But on lots of, on lots of conscience issues uhmmm I think it is right to have, I think it is right to have, free votes... Could we stop for a second. (theguardian.com)