If they just have a different personal value system, there's no tyranny.

The tyranny is when they say, "Because my conscience says X, you have to do Y."

For instance, "My conscience says embryonic stem cells are a baby, so you can't use them in research." "My conscience says you can't eat pork." "My conscience says you can't use birth control." "My conscience says that you can't have an abortion ever." "My conscience says that you can't have an abortion when the fetal heartbeat starts."