The lines were spoken by a man who imagined that he was a woman.
Therefore, I think the comic strip was intended rather about how men can have a skewed perception of women.
The "people acknowledge my existence, people hold the door for me" is not about them being idiots. It's Scott arguing that women have it easy compared to men (which may or may not be true, feminists will disagree).
I suspect this tendency is not correlated to political leaning in any way, and the suggestion that it is says more about how you want to perceive people of a particular leaning than anything about them.
The 6/11/1994 comic about sensitivity training comes to mind. "I can't find my keys" and "my blouse falls to the floor."