Wonder how archive.org fares.
For reference, I’m based out of the U.S. and don’t officially conduct business in the EU. As it stands, I’m completely unbound by the laws. Even EU customers would have to conduct business with me via U.S. dollars on a U.S. hosted server. I.e. they and myself would be bound by U.S. law, as we’d be in U.S. jurisdiction.
That being said, I’m also not hosting “data from An EU citizen”. I have no way of knowing where these anonymous users are posting. If I applied this to people that I can confirm their identities, then sure. However, as it stands, I have no way of knowing who “jcims” or anyone else is.
Article 3.1 states that the GDPR applies to organizations that are based in the EU even if the data are being stored or used outside of the EU. Article 3.2 goes even further and applies the law to organizations that are not in the EU if two conditions are met: the organization offers goods or services to people in the EU, or the organization monitors their online behavior. (Article 3.3 refers to more unusual scenarios, such as in EU embassies.)
You definitely are covered by the GDPR - its just a matter of how and when someone will take action against you.
The second exception is for organizations with fewer than 250 employees. Small and medium-sized enterprises (SMEs) are not totally exempt from the GDPR, but the regulation does free them from record-keeping obligations in most cases (see Article 30.5).