"Personal conscience" refers to an individual's inner sense of right and wrong. It is a person's own moral compass that guides their decisions and actions based on their values and beliefs. Full definition
The party seeks to prevent my candidacy in the next European election merely for taking a stand on matters of personal conscience. (telegraph.co.uk)
You can construct a liberal argument for this, saying that you are protecting the right of individual to withhold their labour according to their own personal conscience. (politics.co.uk)
A good politician can separate personal conscience from public policy. (religion.blogs.cnn.com)