I guess I don't know what proof you require me to provide. I have several children. Only one has a visible correlation between artificial food dyes and abnormal behavior. The others do not. If I had confirmation bias because of food dyes alone, then wouldn't I have the same observation across all my children?
At some point, as the adage says, "Doctor, when I do this, it hurts! What do I do?" ... "Treatment is simple. Don't do that"
I assume that you would agree that allergies are real and afflict some people but not others -- if your son or daughter entered anaphylaxis shock after eating a PB&J sandwich, would you sit there and scold the child- "but double blind studies show, Chunky Skippy is a safe food! This is just confirmation bias!" Why is it so hard to believe that, in this case, artificial food dyes could cause adverse reactions in some people and not others?
It took £750k back in 2007 to administer a double blind study to explore the link between hyperactive behavior in children and artificial food dyes [0] - a study that included Red 40. I don't have an extra $1MM+ burning a hole in my pocket just to prove what I already know with my own kids. Believe what you want, but if consuming neon red food is that important to you, God speed. I will not be feeding it to my one child who has a reaction to it. I avoid it for the others, because.... even though I know they won't have an adverse reaction, what's the point? The dye doesn't make the food taste any different/better.
[0] https://www.southampton.ac.uk/news/2007/09/hyperactivity-in-...