The term litmus test is used in American government to refer to an informal test that a candidate must pass before they will be allowed to take some particular position. It is often said that presidents use litmus tests when they are picking potential Supreme Court justices.
In a litmus test, the potential justice is questioned with respect to his or her position on a given issue. For example, it is said that no Republican president will nominate a justice who is in favor of upholding Roe v. Wade. By contrast, it is said that no Democratic president will nominate a justice who is not in favor of upholding that decision. In short, the justice’s view on abortion is a litmus test that he or she must pass before a president will choose to appoint him or her.
The implication of this is that people who want to hold certain offices are being required to hold certain beliefs (or at least to profess them) if they are to get a chance to hold those offices. In a sense, it is taking away their ability to think for themselves and to hold to positions that they believe in.