The last time I was on a bus travelling out east, there was a Mennonite man who was talking about vaccines with the bus driver. I was surprised to overhear that he was pro vaccine, and that there isn't anything in his belief system that mandates he be anti-vaccine.

So I don't know what drives the anti-vaxx view for Mennonites, but from what this man was saying it doesn't seem to be something that is inherent to being a Mennonite (like blood transfusions for JWs).