From personal experience:
I had a severe allergy to brazil nuts and white fish as a child - which thankfully I grew out of.
This had little effect on me as I avoided foods which contained nuts and fish.
In those days you bought what was advertised on the tin - so flaked almonds were flaked almonds and not peanuts are they (often) are today.
A relation of my father's had an acute allergy to brazil nuts - so much so that she was affected (mainly at Christmas) even walking into a room where brazil nuts were displayed. This level of allergy is, I understand, rare.
Whilst most allergies these days are just trends and fads (bordering on the ridiculous sometimes)
My daughter has a severe allergy to peanuts.
Her allergy is so severe that one peanut would kill her
on the package there was a warning, "caution, contains nuts", problem solved!
This has been more difficult to control as peanuts and peanut oil/products are contained in many things ('flaked almonds'), which is not always apparent - especially if served out of their original wrapping.
She undertook a study as a small child - the doctors discontinued the study after her dose of peanut exceeded one eighth of a peanut as she was in so much discomfort.
It's not nice for the crew and it's certainly not nice for the casualty when they are miles away from an hospital. I'm speaking from experience.
When you've seen your daughter's eyelid coming away from her eyes and her choking, vomiting and at the point of passing out whist you wait for the ambulance it brings home to you the serious effect that allergies can have.
My daughter has always carried an Epipen, as have all the people with whom she has regular contact - relations, school etc.
Has this stopped my daughter travelling - no.
Does she have regular attacks - no.
She is careful and understands that she must avoid foods she is not sure of.
Accidents happen and I understand that the implications in flight could be serious (diversion). But she would not eat unknown foods in that situation so the risk is low.
Would people in other parts of the cabin be affected by peanuts elsewhere in the aircraft - yes, in very rare circumstances.
Should those people fly - ?