I read about this the other day when I was posting about live and inactive vaccines. When it comes vaccines vegans weigh up the risk against the benefit just like anybody else. The Vegan Society defines veganism as
Veganism is a way of living which seeks to exclude, as far as is possible and practicable, all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose.
It's the bit in bold that matters because most, if not all will have been tested on animals and humans at some point and some will have been propagated on chick embryos.
Plenty of vegan mothers allow their children to have the basic vaccinations because they know how terrible the diseases in question can be. A lot of vegans don't like the anti-vaccination reputation vegans have because it paints the whole vegan community as unreasonable or sensible. I think this is an example of the perception that vegans are all very much all or nothing. They probably do more research on subjects than the rest of us before making a decision on something we just go ahead and do.
There was a court case last year in the UK where a vegan mother refused to allow her children to have the regular vaccinations. The children's father disagreed and the court found in the father's favour and the children were vaccinated.