I don't think this is a left- or right-wing issue: Australia was one of the first to ban kids from social media, and Australia is not right-wing by any measure. Canada is hardly right-wing, but age verification is bill S-210 in their parliament.

What you're seeing is a coordinated push by transnational interests; Meta's name has come up in discussions of the funding behind this push. At the very lest, verifying age also verifies that a person is real and not a bot, so advertising firms like Meta will benefit from verification. That's not right-wing or left-wing but rather the influence of business over the political, and neither wing of the spectrum is immune to corruption.