It occurred to me while out walking that this ties in to my previous posts about humor, and being able to make fun of your own as well being a sign of health and reliability. There was a time until the mid-80s, that as hateful to conservatives as he could be, Gary Trudeau of Doonesbury could still make fun of liberals. This allows his usual opponents to sit with him much longer, and sometimes even be influenced, as in Y'now, this time he has a point. That guy IS ridiculous.
My best example has always been Garrison Keillor, who I very much enjoyed even though he was on NPR and clearly preferred liberals. I thought some characterisations of conservatives were over-the-top but I could stay with him. But when the change came, it was in both directions and made him intolerable. He made fun of anyone on the left only in that Reduced Shakespeare Company way, of accusing liberals of being over-intellectual, and his criticism of those on the right went from affectionate accountability partner to vindictive prosecutor. It is not accidental that these changes occurred simultaneously.
It matters, and similarly in serious material where no humor is intended. When you can't turn around and criticise the nutcases on your own side, it is not merely a matter of reduced effectiveness (though that is worth noting), it constitutes ceasing to be reasonable. On the left, it is often valuable to criticise America all the way back through its history. But when you cannot endure hearing even a mild approval of the country that you learned these elevated values in, reflexively pointing out some vaguely-related criticism at every turn, it is not just that you are being insulting and are losing your audience in a tactical sense. It means you have become unreasonable, even stupid, however smart you were when the whole discussion started.