It's technically possible to be more wrong, but you're really pushing the limits here via oversimplifying, changing definitions, and using outrage rather than reason to grapple with the issue while expending the greatest vitriol at something which is largely irrelevant and if anything helps rather than hurts.
(1) Whether neutrality helps the oppressors or the oppressed depends entirely on whether the oppression needs to be actively maintained.
If a neighborhood watch program reporting "suspicious" (i.e. black) people to the (racist) local police is how oppression is maintained, being neutral--that is, not reporting the activity--helps the oppressed.
If a political candidate's main appeal is his anti-trans positions, being neutral (i.e. wanting a candidate who addresses other substantive issues in a competent way) helps the oppressed.
If a system is already in place that will slowly erode the power of oppression (e.g. quality primary and secondary education, and free higher education), then being neutral (i.e. not trying to change the system to erode it quickly and not trying to change the system to stop the erosion) helps the oppressed.
Many, many issues are like this. Neutrality often helps the oppressed. Indeed, neutral treatment under the law is a cornerstone of freedom from state-facilitated oppression. "White people are not allowed to murder black people" as a special rule is a morally questionable edict. "People are not allowed to murder each other" as a general (race-neutral) rule is morally defensible.
Some types of oppression--where the oppressor needs no help whatsoever to continue it, where no law is relevant, and/or where the oppression is self-reinforcing and structurally implemented--are aided by neutrality. Your job as an advocate is to point out when this is the case, and why it's worth the effort to fix this issue this time, out of all the different issues that one could devote attention to fixing.
As a general rule, however, "neutrality favors the oppressor" is awful.
(2) "on the side of" is language that you use when you want to signify that you both know what is going on and have chosen your team.
Are you on the side of the Sahawis or against them? There is no in between. Oh, don't you know who I'm talking about? Well, too bad. You're neutral, and neutrality helps the oppressor. So, I guess you condone human rights abuses and napalming of refugees. Congratulations! Aren't you horrible!
Or, you know, you could understand that there is value in using language to make important distinctions, like the distinction between willful condoning of atrocities, willful ignorance of atrocities, understandable but regrettable inattention, and complete lack of knowledge and any good way to come to that knowledge.
So, are you on the side of the Akyat-Bahay, or against them? Huh, don't know what I'm talking about? Well, I guess you are helping promote theft and home invasions, aren't you?
(3) Stupidity tends to favor oppressors far more than the oppressed, because the oppressors have far more tools to turn the inept bumblings into something that gives them an advantage.
Furthermore, these days, claims of oppression are made without much care for verification that there actually is any oppression. If you assume wrongly that a problem is caused by oppression which is actually caused by something, your solutions are likely to be wildly off the mark.
Additionally, when one is heavily emotionally invested in an issue, rational analysis becomes difficult. One gets led astray by the strength of one's feelings; bias replaces evidence; anything less than enthusiastic support is viewed as hostility and antagonism. When an issue is genuinely complicated, this is a terrible spot to be in, because it robs you of the power to discern what is really going on.
Who comes to the rescue? Why, people who don't necessarily have the character for activism but who do like to understand: those who have the capacity to treat people's lives as an intellectual exercise. Talking to them provides a way to ground intensely felt advocacy in reality, or provides a clue that the intensity has led you astray from reality. Obviously we don't want everyone doing that, because when conditions are bad, someone (many people, perhaps) need to take action to make things better. But, nonetheless, the relatively dispassionate analyst plays a critical role in helping the situation because it is from them that you get the most clear-headed picture of what is going on.
So your outraged attack on them is completely misplaced. For complex problems, that analysis is perhaps the most critical part of coming up with a genuine solution instead of bumbling tomfoolery that would be taken advantage of by oppressors or would-be oppressors.
For instance, if everyone's going around shouting "BLM! BLM! Say their names!" and not paying attention to what the self-styled BLM organization is doing, the corruption and graft there will go unnoticed for longer and the cause will be harmed. You are literally advocating for making things worse so that you can preserve your virtuous outrage.
A more clear-headed analysis would quickly have recognized things like (1) the BLM movement has no legislative agenda, (2) the BLM organization founders have been misusing the funds they've raised, (3) the very phase "Black Lives Matter" is critical but poses a danger of provoking divisiveness, while most successful rights efforts have stressed unity, so a subtext like "Imagine a world where every person is safe" would be highly advisable to take the unity high ground in advance, and so on.
Now, you do have to be wary of the "thinker" who is not actually thinking clear-headedly but rationalizing why it's okay to do nothing. But it's not hard to tell the difference, if you're accustomed to doing any reasoning yourself (or have any friends who are). Rationalizations always end up at the same conclusion, regardless of evidence. Rational thought adjusts the conclusion based on the evidence. A super-easy test that usually reveals the difference is to ask what it would take to get a different conclusion. Rationalizers generally won't give a straight answer, or will need the moon and a unicorn to change anything; rational thinkers will give a measured, sensible answer, or often a set of answers, any of which would do the trick.
Anyway, it doesn't matter if the people thinking about this stuff are going to get involved or not. It doesn't matter whether they're white or black or ChatGPT. What does matter is that problems are perceived clearly, that the downsides of proposed solutions are perceived clearly, that abusive behavior is detected even if it's perpetrated by the "good guys".
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It seems that a good slogan for your approach is: Don't get it right, just fight. A heck of a lot of atrocities are built off of that. Witch hunts. Mob justice against innocents.
Analyze thoroughly, act prudently and decisively. There's absolutely a place for fighting for liberty and justice for all in a visible, obvious way. But don't bash the people and approaches that help you figure out what that place is. And don't bash potential allies because they're not fighting yet. A big part of the job of an activist is to make a compelling case, to move people from neutral to favorable so you can get something done.