We really need to get a handle on what privacy and anonymity mean. As someone who cares very much about privacy, this article just doesn't resonate with me. Thinking in terms of having some singular "identity" means you've already lost.
The title of this post is straight up weird - "The only way of being anonymous is Sweden is illegal". That would imply that if you're walking down the street, anyone has the right to demand that you tell them your government identity? Or if you stop and talk to someone, at some point you need to tell them your government identity in case they're asked about it later? Obviously this is not the case.
The article is really complaining about being able to map between (SSN, name, phone numbers, address). The same mappings exist in the US, and basically everywhere else, regardless of whether mandated de jure or not. To me, the primary concern is not about the existence of this mapping, but about having to spill your well known identifiers in the first place. If I can walk into a store and make a purchase without leaking my name, then the store cannot lookup my address or phone number. And they cannot track my purchases or return visit next week, which is a deeper form of privacy invasion that is generally missed when talking about this concept of singular government "identity".
If I'm signing up for a web account and the website forces me to give my name, phone number, or address (especially in a way that they verify), then likewise I end up connected to my singular government identity just to use a web site. Meanwhile if there are laws prohibiting them from asking such information, or trying to figure it out from IP addresses etc, then I remain anonymous (psuedonymous) to the website regardless of the existence of the mapping of government identities.
I roll my eyes every time I see some news article about a "personal information" leak that merely consists of mapping between well known government identifiers. Especially in the USian context, the more published social security and driving license numbers become, the better! The real concern is the tying of most of your every day behavior to any of those longstanding identifiers.