Updates: I've expanded the first paragraph and added in a second paragraph about Andrew and Bob to better illustrate the situation.
One of our goals is to be welcoming, but our highest priority is to be impactful. We have to be willing to bear a certain amount of negative publicity by people with ideological agendas at times, otherwise we surrender the ability to set our own agenda. Many people have trouble making concessions because of pride. This is indeed a cognitive bias that humans possess. However, we should remember that cognitive bias tend to be adaptive, at least in some circumstances. In particular, pride pushes humans to maintain their autonomy. This is important as unilateral concessions inevitably lead to more more unilateral concessions. At best they provide a temporary reprieve, but soon enough the new status quo becomes the baseline for further negotiation and we should not expect past concessions to be credited by the other side. Taking a realpolitik view, they have no incentive to do so as whatever the situation may have been in the past does not affect the negotiating power of the present. The only exception is for a short time after a deal, lest they destroy any incentive for parties to engage them in negotiation. After this waiting period, previous concession can even be used against you, by suggesting that you are a hypocrite or have failed to deliver on your promises. Further the kinds of people who absolutely refuse to be part of a movement unless condition X are likely to reduce group cohesion and therefore may not actually provide a net benefit.
Even though this may not be perfectly analogous, the following example may make this principle more concrete. Suppose that Andrew and Bob are a couple, with Andrew being stay at home. Bob demands that Andrew have a cup of tea ready for him when he gets home. This is not very much effort for Andrew and although he might not like doing this, he would prefer to do this than to have Bob shout at him. Andrew acknowledges that Bob has a stressful job and that this might help. At the same time, Andrew has a reason to resist this demand because it is a unilateral concession. Surrendering on this point would allow Bob to simply make more demands in the future, since he would know that Andrew can be influenced by pressure. If Andrew has a sense of pride (he is not Bob's slave!), he will refuse the demand. Otherwise, Andrew getting Bob coffee will become the new status quo and hence the new baseline for negotiation when Bob also wants a massage to help destress. To respond to Michael_Wulfsohn's comment, even if Bob does not see their relationship as adversarial (I work so hard for us and Andrew can't do this one simple thing for me! It's obvious that I'm in the right, it's reasonable to try to shout some sense into him!), and indeed even if they both love each other, it still creates a harmful precedent when Bob is incentivised to shout at Andrew next time he thinks that he is in the right, rather than engaging in discussion.
What I would suggest is that middle way, that if we make a concession it is because we have decided that it is the right thing to do or because it is something that is effective in and of itself and not because of illusory and temporary PR benefits. Even in these cases, it may be necessary to delay a change to the point where it is clear that we are making the decision on our own terms, rather than allowing ourselves to be dictated to, as this only incentivises further interference.
This is a purposefully vague warning for reasons that should not need to be said. Unfortunately, this forces this post to discuss these issues at a higher level of generality than might be ideal, and so there is definitely merit to the claim that this post only deals in generalisations. For this reason, this post should be understood more as an outline of an argument than as an actual crystalized argument.
I have decided to post this now as there aren’t any obvious ongoing controversies that it could be directly linked to.
I found this post unhelpful and this part of it particularly so. Your overall point - "don't concede too much on important topics" - seems reasonable, but as I don't know what topics you're referring to, or what would count as 'too much' on those, I can't learn anything.
More generally, I find EAs who post things of the flavour "we shouldn't do X, but I can't tell you what I mean by X for secret reasons" annoying, alienating and culty and wish people wouldn't do it.
"Annoying, alienating and culty and wish people wouldn't do it" - I would like to suggest that this is a bit of an overreaction given that this is just one post and almost no other posts on this forum are like this. It hardly seems like this forum is at risk of being overrun.
Anyway, I tried providing an example, though I still kept it away from directly discussing any concrete issues. Hopefully this makes the principle clearer, even if I haven't directly explained how EA should apply this principle.