Not being funny, but I see this as a breach of privacy. You can buy whois protection on some domains you use for a good reason, not all domains allow it. So you can protect your home personal information from others on the web. Now, they are basically trying to force people to provide that information (like it or not), which I think is dead wrong if you're not selling goods, or offering a paid service. Why should that information be supplied if you only run a hobby site making nothing from other people with it.
Let me offer another perspective.
Lets step back a bit and recall the situation prior to the internet. You want to publish information for the whole world to see. Before radio and Tv, you did so in writing. if you published in a newspaper, the newspaper had a legal address, and the editor would know your address. So, if you wrote utter crap and anyone would want to sue you, they would sue he newspaper, who were responsible for the content.
if you wanted to distribute flyers, you had to print a legally binding address on it to be allowed to do that, again, the person who provided the content was accountable and known.
Enter radio and TV. The rules did not change, radio stations have legal addresses and TV stations have, too. They are responsible and are held accountable for what they are doing.
Enter the internet age. Suddenly everyone wants to be able to distribute his opinion without being able to be held accountable. In germany, you have to provide your contact info on a separate legal notice ("Impressum") for quite some time. If you want to distribute information, you must be able to be held accountable for it.
There is some legitimate concern about anonymity. But the other concern is accountability. And given the way the internet moves more and more to hate-speech, dissemination of fake news and what not, actually holding people accountable for what they do or say is a good thing.
I am not sure the way the GDPR solves this is the best way to solve it, but its a practical way. And for Europeans, having to provide your contact info in your legal notice is a common thing, we already have had that for quite some time through various national laws, its just now codified in EU law and thus gains more reach.
It used to be absolutely normal that when you want to disseminate information, you can be held accountable for it. The thinking that you have the right to say anything to the whole world anonymously is a very, very recent one (20 years, tops). Newspapers still will not print letters they get from readers unless they know the identity of the one who wrote the letter. Yet on the internet, a lot of people just assume they should have this right, and I don't really understand why.
On the other hand, anonymity is a legitimate concern in some areas. For some topics, you simply want discretion. For example lets say you are member of a swinger club. As long as you only visit your local club, you mostly have discretion (but not total anonymity , either - on the contrary, most people will know you). lets say you want to share experiences etc. with other, online. Now, I absolutely understand that you might not want the whole world to know your private preferences. So I absolutely think that you should have the right to register on such a site to share this with a pseudonym. But in this case, you are only a user of a service, you are not the one providing the service. And in fact, the GDPR improves your protection and your privacy in such cases, because it limits what the one running that platform can do with your data, and what data he is allowed to collect in the first place. For users, the GDPR is a blessing (its still not optimal, but it is a step in the right direction).
But as soon as you become a service provider - and yes, sharing information on your blog is providing a service - you have to be able to be held accountable. If you use another blogging platform and spur racial slurs, the platform provider is responsible and will likely take down your blog as soon as he gets the letter from a lawyer that tells him to do so. But the point is: the service provider is accountable and his legal address is known. The same applies to your private page, a legal address for the one responsible has to be known.
I am not saying the GDPR is perfect, far from it. I think some stipulation in it are utterly ridiculous, and I think especially the people running small, non-commercial hobby sites are hit especially hard with this. But its a step in the right direction.
So tl;dr: The GDPR improves privacy for users and makes it easier to hold service providers accountable.