There is some evidence that anti-vac activism was one of the key topics pushed by foreign influence campaigns at several points. I think the simple explanation is that they pushed any topic which could be used for political divisiveness and unrest, but fomenting anti-vac sentiment is especially damaging due to the physical harms it causes.
Looks like Russia did that: https://firstdraftnews.org/articles/anti-pfizer-vaccine-narr...
... and the USA did it too, trying to discredit China’s Sinovac: https://www.reuters.com/investigates/special-report/usa-covi...