There are, in my opinion, two problems with that. The first is that it is very, very difficult for most people to view their own side objectively. The Russel conjugation comes to mind; "I am a freedom fighter, you are a rebel, he is a terrorist." The other problem is that often, calling out your own side's bad behavior feels like treachery. "When arguments become soldiers, to criticize your own sides' points is to stab your fellows in the back." Anyone who engages in that kind of criticism is likely to be ostracized as a traitor well before their criticisms are taken seriously. See, for example, the Hundred Flowers Campaign. I believe the book Scout Mindset by Julia Galef discusses ways around the first problem (I have not personally read the book), with the main thrust being that this is exceptionally difficult to train oneself to do and a mostly personal endeavor. For the second problem, I have no idea except to aspire to groups that welcome self-criticism.
The second problem is being made worse by the increasing polarization and the cutting of the ties that bound the different sides, at least in America. People with political disagreements were never best friends, but there used to be more shared socialization than there is now.
I'm from a bipartisan family in a purple area in a purple/battlefield state. You can't grow up like I did without being exposed to both/all sides of the aisle, so you end up with a pretty decent idea of the follies of your own side as well as a lot of friends/colleagues/etc. that don't agree with you.
10-15 years ago, I was still 'allowed' to deviate from accepted practice/opinion, as long as I respected the hosts, and conditional/partial belonging was allowed. (e.g. I might be a dirty commie liberal, but I'm still a Christian or, on the other end, I might be a gun nut but I'm still queer so I fit in 'enough'). Now, not so much. We also used to have more defined and accepted internal fighting/it used to be accepted that sides were coalitions instead of Borgs.
Now, not so much. We talk a lot about things we can't say/do, and share tips on how not to be pilloried for saying the wrong thing. Interestingly, these discussions are happening with people across all parts of the political spectrum.
People were always somewhat suspicious of you for hanging out with the enemy, but it was accepted if you were of an intellectual or sneaky bent. Now it's not. You're in or you're out.
If you're at a point with your side where any criticism is taken as treachery, you're not really on the same side. Some even think the intention of the 100 flowers campaign was to weed out people who didn't exactly align with Mao (i.e. it was "bad faith" to begin with). Also, the campaign was open to all, not just members of the CCP (Mao's "side" in this context). https://en.wikipedia.org/wiki/Hundred_Flowers_Campaign#Debat...
I think the 'critisize your own is backstabbing' thought is much less relevant in private discussion, and that might be where it's most possible to call out and change compatriots who engage in bad-faith communication.
In high-trust social circles, certainly. But the risk of reputational damage still exists when using these channels; this is how whisper networks destroy people seen as insufficiently dedicated to the Cause. Criticize the wrong person or do so insensitively, do it to a person with an outsized ego, and you may find yourself ostracized. Jo Freeman's essay The Tyranny of Structurelessness well describes how such power imbalances can occur and how people suspected of insufficient loyalty can be informally but firmly removed from the decision-making of a group.
This is, after all, why virtue signalling is such a common tactic. It shores up reputational defense against such accusations. Unfortunately, it also commonly has the effect of further deepening the divide between the group and other parties who might otherwise be interested in the Cause, as the most valuable signalling techniques require costly actions - i.e. ones that are materially or socially damaging to the member doing said signalling. This may affirm loyalty, but often harms proselytization efforts (you cannot advance the Cause to your family if you have cut off contact with them for not already being part of the Cause, for example).
