I didn't have the measles jab in the early 80s because dm noticed that there seemed to be outbreaks of measles which weren't really bad with most children recovering quickly, and outbreaks where it was bad and lots of children were hospitalised/had complications.
She noticed that children who were vaccinated seemed to not get it during the milder outbreaks, but got it during the bad outbreaks. So she concluded that it was probably safer to risk catching it.
We had all our other jabs and she's generally pro-vaccination, so I think it was a genuine informed decision.
There wasn't a mumps jab then, but all girls had rubella at 13yo in our area.
@Benjispruce sorry to tell you that I didn't catch chickenpox off my sister, my friends etc. In fact I was around it lots as a child. I assumed I must have natural immunity, or have had it really mildly. I caught it beginning of my 3rd year at uni, when no one else I knew had it, so much have been a chance encounter. So make sure your dd either gets the jab or keeps away from anyone who has it and doesn't assume she's fine.