It's easy to resolve this discrepancy when you realize these people are not actually liberal or progressive.
No True Scotsman fallacy? I personally give the respect to people to refer them as they would like to be identified. If a Muslim jihadi says he is a jihadi, I respect his self identification and call him that. Similarly, I respect these people's self identification as liberal or progressive.
Huh? Why?
Seriously, I don't understand that kind of thinking. I don't think individuals necessarily deserve that kind of power others. Sometimes we should adjust to save other peoples feelings. But having that as the default seems crazy. What if they are full of shit? Or misuse that power? Or I simply disagree with them.. shouldn't I have the right to disagree with their self identification?