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If they really wanted them down, they'd just do domain seizure. Probably use bots to post lots of copyright material and then just down the domain. Owners would have to file paperwork, with their actual names, or lawyers names at least, to potentially get the sites back.

Theres the argument that sites like this aren't significant enough to matter, but you look at more radical sites like dailystormer, and its easy to see thats not the case at all.

How do you criticize an opponent nation based on their political influence over your nation? Especially when the criticism amounts to "your influence is not just destroying us, your supposed ally, but its harming you in the process"?

On the otherhand, how does that opponent prevent criticism or undermining its influence or reform of its influence?
Label any criticism into an anti-ethnic argument, and then go after it with the same tools used against gangs/terrorists/criminal syndicates.

It's a hard problem, and what the actual problem is, is regulatory capture.

Effective absolute power, relative, or in-practice, eventually destroys those who wield it. Every. single. time through history.
Be it economic, military, religious, cultural, or political power. Every group that has ever held absolute power was eventually destroyed by it. Not "in spite of it", not "because downfall is inevitable anyway", but precisely because of the inherent contradictions it introduces to any dynamic system.

One way of looking at it is from an opponent's perspective that has already realized this at an organizational level:
How do you pass off, or give up power gracefully, without inviting the very destruction you intend to avoid?

Cultures don't drive organizations, organizations drive cultures. That was foucault's basic realization when he talked about institutions as 'praxis', though pardon me if I'm huffing my own farts here. It was the reason for the long march.

This is tangent to your discussion about sites like this being controlled, allowed, or even hosted by mil-intelligence (foreign or domestic) but also I think it is of primary importance.

The mode of communication changes in a society before the organization of society changes. A key example of this was the use of trader's as messengers. It allowed us to transition from pre-roman city states to empire. It allowed the consolidation of pre-iron age china into dynasties.

But the centralization trend in communication has now reversed, in accordance with the technology, which I think it really a signal of all the ancillary decentralization changes that world powers are currently fighting against (demographic and political for example).

Between social organization, and the mode of communication, is another step: the mode of the spread of ideas.

It's now, for the first time in 200-500 years (depending on the level you're looking at, the region you're looking at, and the institution), horizontal and distal in nature.

It means theres a specific reason we keep seeing 'our' ideas spread while we consistently get hit with the message that "nobody is listening and what you talk about it irrelevant."

Officials, executives, the executive bodies of NGOs, institutions, corporations, political advocacy groups, are all feeding on eachothers ideas, which because of the need for counter-opposition, includes the collated "intelligence" they get from trolling and backing up sites like this, 9gag, poal, flingup, gab, etc. The proof itself is none other than the commercial companies that now exist to do "threat intelligence", basically monitoring these sites. And the inadvertent larger effect is, while these larger institutions may not directly listen to us (discounting the stray executive who is an anon-user and may be influenced), is that these institutions do listen to eachother and the experts they hire for 'analyzing existing and emerging threats' (us apparently).
Effectively this becomes a way of laundering our message, and I don't think they've actually fully realized it yet.

The problem they're dealing with is something called an info-hazard, or somesuch, but can more broadly be described as an 'emergent centers of soft power', however minor in nature, though thats probably an inexact description of the underlying phenomenon, because emergence implies something thats stable, rather than a temporal effect of system dynamics. The conclusion remains that technology, on a meta-scale, is a forcing-factor for this effect, so its not going to be changed through otherwise-sophisticated social engineering based on network analysis which they typically rely on now. And the more they try that, the more ground they will (gradually) lose long term. In otherwords they've reached the limits of the effectiveness of their existing methodology for control, and if you're looking at it from a high enough level like i'm doing right now, you'll see the immediate correctness of the model.
Its why I wrote in earlier predictions that for example, israel and judaic culture, despite surviving for five thousand+ years could cease to exist as an effective force in as little as the next three hundred years. They've over-adapted to a communications environment that was stable for thousands of years, and that same environment is now going away, but I'm digressing. I think some rabbis probably realized this a long time ago and that was the reason for a switch to matrilinealism, to force integration without being explicit about it, but looking at it, what it means is that on a long enough timeline, all they did was delay the inevitable. Anyway I'm getting sidetracked.

The simpler hypothesis, which typically I would accept on the grounds of being more straightforward to begin with, is that
messages we ourselves (as a sphere-of-influence, the 'alt right', the 'radical middle' etc), thought we created or spread,
were infact created by the regime and given a boost. Concepts like accelerationism, memetics, etc.
Whether this is true or not is ancillary though, because in the current mode (horizontal and distal spread), you end up with feedback effects that have a vanishing horizon of origin, meaning after a while, not even the source of an idea can be sure where it originated. It's part of the problem intelligence agencies are facing especially today, not merely too much information, but too much dogfooding their own bs they've spread around the world like a game of telephone thats grown too large to manage.

They've basically reached the upperlimits of the complexity they're able to manage effectively. And they're now in the diminishing-returns phase of organizational techniques. It's also why I predict more totalitarianism in the future and not less. When the smooth velvet glove of soft-management fails to pursued people through its sundry manipulations and influences, the glove comes off to show the iron fist underneath.

The idea of 'nudging' the public is failing, even as it appears to reach its peak success, and network-based techniques aren't going to fix it.