If for some reason you believe "obligation of operators to register establishments" would apply to individual pet owners (I don't believe it does, as earlier in the document "pet keepers" are separate from "operators") - there's a clause to allow exceptions: "Member States may exempt from the registration requirement certain categories of establishments posing an insignificant risk"
The only thing in the entire document that applies to "pet keepers" is ... [to] be responsible for:
(i) the health of kept animals;
(ii) prudent and responsible use of veterinary medicines, without prejudice to the role and responsibility of veterinarians,
(iii) minimising the risk of the spread of diseases;
(iv) good animal husbandry;
There are some further restrictions to do with moving pet animals between member states
I'm trusting here that the Dutch minister of agriculture is being accurate in her letter to parliament describing ongoing issues [0].
0: https://zoek.officielebekendmakingen.nl/kst-28286-1062.html
"For example, holders who only have a few pieces of poultry must also comply with requirements for I&R and there will also be obligations for holders of animal species for which no requirements currently exist, such as bees, bumble bees and camel-like animals. The Netherlands has argued against these requirements when drafting these new regulations, but received little support from other member states and the EC. The EC indicated that it can allow Member States to grant exceptions to these obligations."
So it's up to member states if they want to require owners of pet chickens to register them
OK, so what's the problem? After all, this won't come into effect until about a year and a half from now and it seems that there is agreement that there should be exceptions.
Given that, what makes you certain that there won't be exceptions?
> is currently trying to arrange for exceptions
You seem to be certain that this will not succeed. Why?
> It is not fake news.
Hmm...it's not in effect, there seems to be some agreement that there should be exceptions and exceptions are being worked on. ¯\_(ツ)_/¯
I don't know what will happen, but this situation is concerning to many people. Also consider that the news plays a role in policy making (for better or worse), i.e. some added pressure from advocates may help to get the needed exceptions in place.
As for the chickens: you are linking to what look like current regulations in Germany. At issue is the Animal Health Regulation (https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=OJ:L:201...) which will be in effect from 21 April 2021.
There is a statement that there should be exceptions for pet animals, but these exceptions did not make it into the regulation for chickens. The Netherlands argued for this but did not find support, and is currently trying to arrange for exceptions. It is not fake news.