"opt-out as default" in the context of GDPR means that all EU citizens have to be considered as not having given consent to usage of their personal data until they explicitly do so. See Recital 32, Sentence 3: "Silence, pre-ticked boxes or inactivity should not therefore constitute consent." [0] in the context of consent of the data subject to make processing of personal data lawful (Article 6 [1])

I'd be glad if you could point out a regulation on the content website owners must offer to people who do not wish their personal data to be processed.

[0] https://gdpr-info.eu/recitals/no-32/

[1] https://gdpr-info.eu/art-6-gdpr/