At that point, the progressives will do what they have always done  They're never happier than when they are demonstrating their moral, political, and religious purity by heading for the exit and starting their own small but pure church or party.
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Progressives like to flaunt their moral and political plurality by splitting off and making their own party or church.
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Political or religious purity doesn't matter to progressives because they'd rather have one contiguous party that wins elections.