I don't think they use peanut oil as an adjuvant.
Here is my impression of what is going on, in some cases.
Aluminum is in the vaccines to put the immune system on high alert. Without the aluminum, the immune system would notice the attenuated bugs and just shrug. Why bother? But with the aluminum, even feeble bugs look dangerous and provoke an immune reaction.
So, okay, you take your kid in for a vaccine and you just happen to have had a peanut butter sandwich that day. Your baby got a bit of the protein in the milk (is that possible) and then the aluminum kicks the immune system into high alert, and it goes OMG, look at this nasty stuff, and flips out over the peanut trace.
And it isn't just peanuts. There are more and more people who are extremely allergic to all sorts of stuff. I had a friend who could die from a bit of fish.
But I'm no expert. This is just my impression of what might be going on.
I also have a general sort of feeling that sending baby immune systems into high alert mode, over and over again...might be sort of a bad idea. Might mess them up somehow.