I agree with Eugene Volokh that the charge of “hypocrisy” – literally, playing a role – is way overused in political debate. Whether someone else sincerely believes what he says is not, generally, relevant to the question. Often enough, what seem like inconsistencies in an opponent’s position reflect no more than one’s own reluctance or inability to enter into the other’s thought and find the principle or interpretation that reconciles two apparently inconsistent views.
Still, consistency remains a bedrock logical principle, and pointing out genuine inconsistencies remains a legitimate form of criticism. For example, people who defend the “religious freedom” of employers to deny their employees insurance coverage for reproductive health, but not the freedom of Muslim congregations to build houses of worship, may reasonably be charged with twisting the idea of “religious freedom” all out of shape. If what they mean is that they want the freedom both to practice their own religion and to prevent other people from practicing theirs, then (despite the precedent set by the Puritans) their views may properly be called “un-American,” and their pretense to be defending “religious freedom” in the generally accepted (and Constitutional) sense of the term stands unmasked as dishonest.