How to find hotels in Europe which allow for anonymous check-in?

The short answer is: there isn't any.

There is no such thing as anonymous booking nor anonymous check-in. What you have described is simply automatic collection of keys on late arrival or arranged/instructed by the hotel. Just because some European countries have lenient regulations it does not mean that they encourage anonymous stays. There is an implicit trust involved that the person(s) who are staying are the person(s) who booked in the first place.

At a more detail level, your example of German hotel is misintrepation, rather confusing trust with anonymity. While the German laws are notoriously protective of customer data, the registration is still mandatory, as also reported by KPMG. Also, a report by U.S. Department of Homeland Security clearly mentions the "EU practice of mandatory collection of hotel guest registration data" as well as potential possibility of data sharing in future.

A similar discussion thread, on FlyerTalk, might be of some relevance.

I strongly discourage you to use a hotel or residence in EU with a (false) hope of anonymity for whatever reason.

For general sake of convenience, you can try peer-to-peer rental agencies that support anonymous currencies (bitcoins, etc), such as 9Flats. Still, if using bitcoins, while the transaction is anonymous, the hosts and guests are not, the general data collection laws apply, and as 9Flats says it is built on "mutual trust."

Disclaimer. I am neither a privacy nor legal expert. The above information was collected simply by a quick web search.

I know that some starwood hotels allow you to entirely skip the check-in process and simply walk up to your room and use your mobile to unlock the door; although this isn't anonymous.

I also know of some hotels that allow you to check in as an alias; but again, this isn't anonymous this is just an extra layer of privacy to prevent people from asking for you by simply calling the reception. It is also used as a layer of security by some.

Truly anonymous clandestine checkin - where you simply open a door, walk up to the key rack, pick up your key and go off to your room, if there is such a place, I would definitely like to visit it.

It may have been possible years ago, but this day of cross border terrorism and whatever else, data collection has become a sort of fever for any and all jurisdictions that hope to attract any kind of tourist dollars.

You may have been able to do so previously, but I doubt you can today:

1. Even if you use a pre-paid anonymous card, or have someone else pay for your room booking, you need to show proof of who you are when you arrive to collect the keys. The name on the reservation has to match the person asking for the key. This name can be an alias, but that is not the definition of anonymous.

2. Further, it goes towards security and liability on the part of the hotel. God forbid there is some incident - say a fire or other such security issue, they need to know who is checked in where, who is accounted for, etc.

3. As mentioned by others, some jurisdictions mandate collection of hotel guest data as part of their overall security procedures/requirements - if they don't they are breaking the law and may be subject to fines or worse suspension of their license to operate.

It may be true that you are able to skip a lot of this formality if you use more informal means of stay (like airbnb, hostels, or staying with friends/colleagues; room sharing) but I don't think that was in scope of your question.