Once again, Archbishop Chaput confuses American conservative orthodoxy with Catholic orthodoxy.  To be sure, the two overlap in part, but they are not the same.  While he criticizes others for their promotion of secularizing the culture, he does the exact same thing by promoting American political conservativism. For him to single out political progressives/liberals and suggest that they leave the Church is clerical/episcopal malpractice.  

An orthodox Catholic is one who roots his or her life in Christ and seeks to follow him.  There always has to be an understanding that one will never get this right, and will always be in need of reconciliation.   That is why Pope Francis consistently preaches about the importance of accompanying those who have lost their way.  That is the mercy of Christ in action.  In this instance, I sadly do not see Christ in Archbishop Chaput, but a shill for American conservatism.  That's not orthodoxy.  However, I don't think he should leave the Church.