I'm exhausted but I'll try and take a swing at this, speaking as a long-term ex-anarchist. Note that I can only speak for myself but these are the trends I observed and a lot of this is exactly what I experienced.
So in transitioning from progressive liberal to the radical left, it's basically a rite of passage to identify all the ills and the egregious excesses of the government and corporations. I think this is not only valid but it's also extremely important.
The problem that emerges is that anarchists and LibSocs can fall into a trap of universalising this very valid skepticism to expand to all forms of hierarchy that have existed and will ever exist.
This is going to sound uncharitable but it's really not intended to be this way but I see a deep form of liberal hegemony as being not a positive form of hegemonic ideology but a negative form of it. Let me explain: the USSR established its own cultural hegemony. It was very much a positive cultural hegemony: this is who we are, this is how we act, this is the future we are striving to achieve etc. etc. You absolutely see this in Soviet art and film and propaganda.
The negative form of cultural hegemony that I understand liberalism to mostly rely upon, especially in a post-Gilded Age era or a neoliberal era or wherever you want to draw that line, is epitomised by Francis Fukuyama's pronouncement about arriving at the end of history; this wasn't a positive proclamation but rather it was a negation of the future, of the need to strive for a better world, of the demand to be better. Instead it was essentially an attack on and an erasure of aspirations.
This is also seen on a small scale with people demonstrating antipathy towards unionism; "they're all corrupt", "they used to be important in the past but there's no use for unions anymore", "there's no point joining a union because I'll just get fired or management will close this branch down if we all unionise". That sort of thing. It's also seen in the shadow cast by this plethora of pseudo-choice we are offered and, forgive me for invoking Horkheimer & Adorno but, the pseudo-individuality inherent to this developed form of capitalism we exist under. There's no point boycotting because how do you avoid consooming products from one of the two or three oligopolistic companies that have cornered a market? Why bother attempting to divest from BlackRock when they already own everything? Why bother protesting against war when we know the government is going to ignore us and prosecute it anyway? etc.
So this negative form of ideology or liberal cultural hegemony tends to inculcate the belief in LibSocs and anarchists that the best we can really achieve is abolition of the current state of affairs and not the construction of a positive project to bring about the revolution.
This is where I take issue with Audre Lorde, or at least the way that people quote her and what this is used in service of. She is absolutely right that you cannot dismantle patriarchy with patriarchy or that white supremacy will not be dismantled by a different form of racial supremacy. I think the distortion of Lorde comes with people thinking that this quote is in service of abstaining from using some of the most valuable tools available to us; you cannot hug the violence out of the bourgeois state no matter how hard you try (just ask the hippies). But at the same time I think we need to be cautious about how far we take this message; people can arrive at pacifism simply because the bourgeois state uses war and violence, if you took this to the the point of absurdity you could imagine people rejecting construction itself or maybe even hammers because infrastructure has been used to enact genocide and land theft and vast exploitation through colonialism and imperialism in so, so many countries. Heck, hammers have been used for DV and assault so you wouldn't want to taint yourself by benefitting directly from that instrument of violence, would you?
But it's very easy to slip into a reductive or reflexive rejection of things like the state simply because most states have historically been dogshit. If you look exclusively at the west from the advent of feudalism to today, it's basically all of them.
This is where anarchists tend to develop the basis of a quite bitter ideological distinction from communists, although obviously this varies in degree depending on what sort of anarchist we're talking about here. (I'll try to remember to circle back on this negative urge and how it provides a degree of... I guess ideological comfort or safety for anarchists once I've finished the other parts of this comment.)
The other factors are a disagreement on the pace of the post-revolution construction period (which likewise comes from the difference between materialists orienting themselves to addressing material conditions and working to resolve contradictions and anarchists who mostly prefer abolition as the means to address these issues) and the other one is that anarchists tend to be exposed to convenient historical narratives that are overly reductive if not downright anaemic.
So for the pace of the post-revolution construction, most anarchists expect a very swift transitional phase - the abolition of capitalism, often the abolition of markets themselves, prison abolition, and all sorts of other things to establish a more-or-less horizontal or low/zero hierarchy society. Again this depends on the different types of anarchist in question but to put it simply they tend to believe that post-revolution you knock all or most of it down, then establish a government or council of sorts (which again varies) and you call it good.
So from that perspective, communists get into power and instead of following what anarchists believe to be the correct path, instead communists go completely the wrong way and even start building up more state than existed under the Tsardom, for example. With this in mind I think it's easy enough to understand why they perceive this to be a betrayal of principles and of the revolution.
The last thing I want to touch on is the historical narratives. Anarchists have a tendency to share a distorted perspective on historical moments; the communists betrayed the anarchists in the Spanish Civil, the Bolsheviks stabbed the Black Army of Makhnovia in the back, occasionally you'll hear discussion of the KPAM likewise being crushed by the Soviets (although not very often tbh).
All three are actually very complicated topics and there's a lot to cover with them but in broad brushstrokes the narrative is that the communists were the aggressor and that they opted not to leave the anarchists alone to do their thing because they wanted to crush the true revolution. I disagree with this narrative these days, although I didn't always disagree with it.
There's a really good article by Jones Manoel on this sort of preference for martyrdom-over-statecraft mentality here. While he only discusses western Marxists, it definitely applies to a lot of anarchists and LibSocs. I think that Manoel simply doesn't regard the latter two as worth addressing though.
So we've got the martyrdom and purity fetish for the immaculate revolution covered there. Last of all to circle back around to the ideological comfort of the negative, I've seen plenty of anarchists do this and I have definitely been guilty of doing this myself - by not supporting or critically supporting any but the briefest attempts at revolution (and then only maybe 3 or so of those), you can create a rhetorical and ideological detachment from the real world attempts. You don't have to engage or defend anything, you can just reflexively dismiss things as being statist or hierarchical or authoritarian and thus you don't have to grapple with the reality of their circumstances or to consider what would be a better way of resolving the contradictions or moving forwards with the project. "You committed the sin of statism? Then I can wash my hands of you and that's that."
This is alluring because it's a simple rubric and you don't need to wrestle with the reality of things. To put this into an analogy that's probably more relatable, imagine a Marxist who refuses to engage in the ol' agitate/educate/organise because "liberals are social fascists and counterrevolutionary - I'm not gonna waste my time befriending my enemies!"
On the face of it, there's nothing false in that statement. But the application of this line of thinking absolves this Marxist from needing to do any of the hard work because they have created a rhetorical and ideological detachment from the most important task that a revolutionary faces and so by abdicating from this duty they never have to put in any effort and they never have to deal with fuckups and failures and addressing their own inadequacies.
That's a pretty close match to this urge that exists in a lot of anarchists and it's also why they can invest a lot into their grudge against communists, because ultimately the other option is to engage in the hard work of listening and learning and working with/working on the "authoritarians".
Obviously all of this is my vain attempt at brevity so I didn't cover the broad terrain of different ideology tendencies within anarchism and I'm talking specifically about the anarchists who really bear a grudge against communists. Plenty of anarchists do not begrduge communists and are very willing to work with them and to engage with them (or to roll up their sleeves and engage in the difficult work of educating, agitating, organising as well as grappling with the historical realities fafed by revolutions) so I haven't given consideration to this cohort of anarchists because it's beyond the scope of the question, although if I gave the impression that what I've said is true for all anarchists then that's on me.
The person who tweeted this, Jake Hanrahan, isn't someone I trust and I'd encourage other people to be cautious about him and his work. He's too cosy with the agents of imperialism, he doesn't strike me as a person who is anything more than aligned with the left (mostly) due to opportunism, and personally I'm kinda waiting on his Tim Pool arc.