I think this post is fairly uncharitable to ACE, and misrepresents the situations it is describing. My overall take is basically along the lines of "ACE did the right thing in response to a hard situation, and communicated that poorly." Your post really downplays both the comments that the people in question made and actions they took, and the fact that the people in question were senior leadership at a charity, not just random staff.
I also want to note that I've had conversations with several people offline who disagreed pretty strongly with this post, and yet no one has posted major disagreements here. I think the EA Forum is generally fairly anti-social justice, while EAA is generally fairly pro-social justice, so there are norms clashing between the communities.
The blog post
Taken at face value, these claims seem pretty absurd. For example,"inextricably linked" implies that societies without white supremacy and/or patriarchy wouldn't oppress animals.
Your main issue seems to be the claim that these harms are linked, but you just respond by only saying how you feel reading the quote, which isn't a particularly valuable approach. It seems like it would be much more productive to read the source document they cite than take your personal reaction as good evidence about the value of the claims.
In this case, I think many authors have made this particular argument, and it isn't some out-there claim. If you think it is a good argument, then you might have good reasons to work on both these issues. If you think it is a bad argument, then you might still have good reasons to work on both these issues, as the harms from both could be pretty severe.
I'm not particularly certain how social justice work (especially US-focused social justice work) ought to fit into a very strong EA framework, but nothing in this struck me as unusually strong language from a social justice perspective. Plus, ACE removed the blog post, which might be a tacit rescinding of their support of the claims made in it, so it doesn't seem like this is particularly good evidence to your point.
Withdrawal from the 2020 CARE Conference
This section, which seems like the bulk of your argument, strikes me as being quite misleading about what happened.
From my perspective, these so-called "inflammatory" and "harmful" comments were generally respectful in tone and expressed pretty reasonable views -- certainly nothing that should be considered outside of the overton window of EAA discussion.
The comments in question are undeniably inflammatory - they started a multi-hundred comment argument in a Facebook group, which as far as I know is the only thread that the moderators of that group have locked (at least in recent memory). There were also dozens of people in that thread, all of whom strongly thought that the person in question and others were being harmful, so your sense of the overton window for EAA discussion (given that the forum is the main platform for EAA discussion) seems like it is miscalibrated.
You also neglect to talk about the specific things that the commenter in question did or said, and fail to acknowledge that multiple commenters were country-level Executive Directors of Animal International, not just random staff.
It seems like what happened is as follows:
One could reasonably disagree with some of the comments that the planned speaker posted, but his comments seemed far from anything that would reasonably make people feel unsafe at a conference, and very far from something that would justify barring him from speaking. So I'm very concerned that ACE is implying that the CARE organizers made a mistake in letting this person (who ultimately withdrew from his scheduled talk) speak at the conference.
I think that there are two things wrong with this.
Penalizing charities based on statements from staff
This section severely downplays that the staff in question were both country-level Executive Directors of Anima, and were in senior leadership roles. I think if ACE is exclusively penalizing these charities based on their statements, it is entirely reasonably to do so given that they lead large wings of Anima. And note that ACE still recommends Anima as one of their Standout charity recommendations. They still urge donors to support Anima. They still do fundraising for Anima. They haven't cancelled Anima or something.
I'm not trying to say that ACE's culture review is perfect or to justify their review of Anima. Like you, I don't have enough knowledge of how that process works to evaluate it well. It seems good that they want to include this evaluation, and I imagine that it is incredibly hard to do well. I imagine that it is reasonable to design a survey, and when you realize that it doesn't capture everything you want to capture, you weigh up your survey results against outside information you're familiar with and use that to make your assessment.
The supposed harms of this action
Embracing social justice norms may lead to less effective allocations of movement resources.
I could see this going either way - maybe the lack of representation of non-white people in the animal movement is a weakness that is making it less effective. Maybe if the organization stands up on multiple issues you care about, you're happier at work, and end up being more motivated at work. Maybe social justice norms are just good, and a minor trade off in effectiveness is worthwhile to have a more equitable world. This doesn't seem like an obvious harm to me, and we don't have particularly strong evidence in either direction.
Embracing social justice norms may attract bad actors
This just seems like pure fear-mongering. There is no evidence this is happening, and it is really dismissive of funders' and grantmakers' ability to evaluate projects. If I am making a grant, and it is an animal program, obviously I'm going to think about the impact on animals.
Also, say that if this is true - then it is probably equally likely that embracing anti-social justice norms might also do this, and it seems like the bad actors on the anti-social justice side are much worse (though note, I'm not convinced that most people in the social justice community who might do this are "bad actors". They are probably just people who disagree with you about the effectiveness / importance of their project - people on the anti-social justice side of things seem much more likely to be genuine "bad actors". This isn't to say that the social justice community is perfect or the discourse norms are great, but I guess it seems like the far-right is a lot more harmful than the far-left right now, even if the far-left has more cultural power).
Embracing social justice norms is likely to create a hostile epistemic environment and reduce trust
This is again, equally true in both directions. I can say right now as someone who is fairly social-justice sympathetic that I'm not very comfortable writing my opinions on the EA Forum about these things, despite them being (I believe), pretty rational, well-reasoned opinions. And I'm a white man. I can easily imagine that if I were a non-white person, I could be completely alienated from this community. Imagine that you're browsing a forum, and see that there is an event for how people not like you could support people like you in a space where you've been historically underrepresented / mistreated, and then seeing a leader in the space endorse a comment that the organizers of the event are a hate group. We already have a hostile epistemic environment and reduced trust — you (Hypatia) just happen to be on the inside already.
I'm not trying to argue that ACE did everything perfect here, and am definitely not claiming ACE is above criticism for how they handle charity evaluations, equity issues, or anything else. I think ACE definitely did not communicate on these issues well. That ACE did what seem like totally reasonable things to do, yet they made you and many other people in the EA community upset by how they talked about it demonstrates that they failed to communicate to all their audiences well. But I think your post is a strong mischaracterization of this situation, and represents a really uncharitable position toward both ACE and social justice work.