If there's a minimum amount of Evil that must be maintained, and the neutrals are maintaining that evil, then they are protecting and encouraging evil to exist, and fighting Good to do it.
Which is, y'know. Evil. Killing good people who seek to stop murderers and other forces of evil is not a morally neutral act.
In my proposed thought experiment, the Neutrals aren't maintaining Evil. Some amount of Evil will always exist, without needing anyone to maintain it. And at no point was it proposed that Neutrals go about killing Good people.
The key phrase is "According to this worldview".
The Neutrals think they're not doing evil. Or that greater evil will come from it. However, the neutrals in this thought experiment are a bunch of gibbering fools who are committing evil acts in defense of evil while thinking that will somehow keep things 'Balanced'.
Internally they may believe their actions are good (which tips the scales to good, I guess, and breaks the balance any way you slice it) but they're actually just allowing evil things to happen and stopping anyone who tries to stop those evil things from happening.
There's no requirement that Neutrals commit Evil acts. Nor is there any requirement that Neutrals believe they are Good. Neutrals oppose Evil (possibly for selfish reasons) without also seeing the necessity of Good as defined in the OP (they could, for example, beleive a pragmatic society built on enlightened self-interest is more sustainable and beneficial than one that requires universal altruism.)
"Muscular Neutrals" are -absolutely- allowing evil to exist. Because Good seeks to destroy evil and Muscular Neutrals step in to stop them from landing the killing blow.
Muscular Neutrals aren't preventing Good from landing the killing blow. Good is and always will be incapable of landing the killing blow, and there's nothing Neutral can do about it. Muscular Neutrals are preventing prideful people with Good intentions from dealing collateral damage.
If Neutrals just didn't get involved and let good and evil fight it out, they'd -still- be allowing Evil to exist by not opposing it and helping to squish it. They also wouldn't be "Muscular Neutrals" because the whole thought experiment hinges on these neutral entities -acting- to preserve the balance.
I.E. Defending Evil when Good might win, and defending Good when Evil might win. To "Maintain a balance".
That's not the definition of Neutral that I'm proposing. Neutral isn't trying to prevent Good or Evil from winning. Neutral has come to the realization that it is ontologically impossible for Good or Evil to win, so Neutral acts to prevent either side from causing (intended or unintended) collateral damage to bystanders.
And this is the external "Something bad happens if evil is destroyed" outcome I was suggesting.
Technically, in my thought experiment, Evil can't be destroyed. If I was interpreting you too literally, and you are using "something bad happens if evil is destroyed" as a stand-in for "Good actions can have bad consequences," then I concede my argument. I absolutely agree that Muscular Neutral only works if it's possible for Good actions to have bad consequences.
In which case they're performing Evil actions against Good people to prevent a great external Evil. Which is a "Good" thing for their internal worldview, which unbalances good and evil, soooo... Not striking a balance, which is the intent of "Muscular Neutrals"
(Just including this last part of your post for completeness. I've already addressed it above. Muscular Neutrals don't have to believe they are Good. They just have to oppose Evil for whatever reason.)
But that is just an example of what they said...?
You have redefined Good so that it has evil in it. "Any attempt to make the entire world better will inevitably make it worse" IS "Good isn't actually Good, it just thinks it's Good, but it's actually Special Purpose Evil With A Lot Of Hangups."
The "muscular" Neutrals are thus the actual Good faction, trying to prevent both of the two squabbling Evil factions from winning--assuming they're correct, I mean. If they're incorrect, then they're the ones who are Special Purpose Evil With A Lot Of Hangups. Or...
...what she already said.
I don't believe I'm redefining Good. I'm using the working definitions of Good and Evil provided in the OP. To paraphrase what Good and Evil mean in the proposed thought experiment:
Good = altruism and respect for others
Evil = harming and oppressing others
Note that these definitions of Good and Evil don't require Good to be "that which produces the best outcome for everyone." In fact, a Good character (who is genuinely altruistic and respectful of others) can cause Evil outcomes (which result in harm and oppression) without willfully taking any Evil actions. Being 100% Good provides no guarantee that one's actions produce beneficial results.
Good characters fight to protect the dignity of all sentient beings. Evil characters fight to harm or oppress anyone who gets in their way. Muscular Neutrals fight to make sure all these non-Neutral parties are going to war wielding Nerf weapons, so bystanders who get caught in the crossfire are merely bonked on the head, instead of being maimed or killed by idealogical warriors.