I doubt making a website available on the global internet would be seen as "doing business in the EU".
Article 3(2): This Regulation applies to the processing of personal data of data subjects who are in the Union by a controller or processor not established in the Union, where the processing activities are related to: (a) the offering of goods or services, irrespective of whether a payment of the data subject is required, to such data subjects in the Union; or (b) the monitoring of their behaviour as far as their behaviour takes place within the Union.
https://en.wikipedia.org/wiki/L%C3%A8se_majest%C3%A9_in_Thai...
I suspect what we'll see soon is a law protecting US companies from EU overreach, comparable to the SPEECH ACT.
https://en.wikipedia.org/wiki/SPEECH_Act
It would not surprise me if some US companies are holding back, because they expect similar protections from foreign law to be passed here.