Within countries, anti-vaxxer sentiment tends to fall with rising IQ (e.g. white males with no degree see no difference in risk between contracting COVID-19 and getting vaxxed, barely higher than the numbers for Blacks and Hispanics, while Whites with a degree give the factually correct answer).
However, between countries, there seems to be no such correlation.
If anything, it is an inverse one.
To take a related example for which we have international polls, the countries of the Third World almost universally support vaccinating children, while the countries with the most anti-vaxxer sentiments famously tend to be an odd medley of First and Second ones (most notably, France, Japan, and the former USSR sphere).
Why the difference?
Probably the most obvious one is that so far as many Third Worlders, it’s a clear-cut case of whom to believe, Internet conspiracy people or their lying eyes (namely, having had vast mortality reductions through suppression of once endemic diseases within living memory).
In the industrialized world, both the first world and most of the former socialist bloc, this process happened much earlier and has become part of “background” life.
It is thus an issue that has been largely relegated into the realm of political signaling, e.g. displaying disaffection with the Establishment (rightoids and hippies in the West, sovoks in Russia… I don’t know who their equivalents are in Japan).