Without judging this or trying to axiomatically derive the logic, I think the claim here is that a/I knowingly and deliberately provides services to the PKK, which the US and the EU designate as a terrorist organization.
My understanding is that this is only coming from the US government. Do we have any reliable information to back this up? Because if it's just the US government, I can safely assume it's all lies.
It’s more than that, I think. I read through the various government statements as I was curious about rationale and precedent: the other two groups impacted by the order are rather unambiguous extremists, so understandable. In the extended justification for this a/I group, the US gov lists a large number of US and EU “Antifa” groups that variously leverage their services, including one that the individual recently arrested for wiping his phone is meant to be connected to. It suggests to me this was the result of some considerable network analysis and that the intent is to now have stronger legal tools to go after those groups.
I think that second (speculative, of course) step would be the more worrying precedent: if the use of technical infrastructure also used by designated groups was formally made to be incriminating/right-waiving. Why wouldn’t that apply to Signal, for example? The OP suggests the dividing line should be between true infrastructure open to all, including unsavory actors, versus tools that advertise services to a particular faction. It’s not an entirely disagreeable distinction, but I think in practice it’s rather fuzzy (Moxie of signal is/was rather far left himself, if I recall).
EDIT: Re-reading the document, the state department emphasizes that a/I “manually vets all potential users.” OP’s distinction stands for now.