MSG was the first taste bud science was able to isolate on the tongue because MSG is a messaging enzyme in neurochemistry and it turns out that the taste bud very physically resembles the brain receptors. In a similar way to caffeine, the brain requires a moderate amount of MSG to function, but can easily be over-stimulated.
The reason for all the "perfectly fine" "controversy" with MSG is that there's still no known allergy to it, and the early proponents of "MSG allergies" were quacks using bad science for racist reasons (despite it being a naturally occurring substance, and a required enzyme in the brain).
So overall it is much less controversial to say that MSG is a known migraine trigger in some people. It's still "safe", migraines so far as we know are rarely life-threatening even if sometimes you do feel like you are going to die. You mostly just need to acknowledge that as a trigger it varies greatly among people.
The analogy to caffeine is an extremely useful one as caffeine is also "generally recognized to be fine/safe/not an allergy", but too little caffeine and too much caffeine (and caffeine withdrawal) can all be migraine triggers or migraine relievers depending on what side of it you are on. (Most over-the-counter "migraine medication" if you check the ingredients is just a dose of generic Tylenol and a shot of caffeine because the most common migraines in America are often the withdrawal state or the too little state and it isn't likely to make it worse if you are in the too much state already, unless too much is on the edge of a caffeine OD and you have more life threatening problems.)
It plays the other way sometimes too: sometimes I crave foods high in MSG when I have a migraine and that will settle the migraine some.