Just because it's a neurotransmitter in your brain, doesn't mean it can't have adverse affects elsewhere in the body (conversely, there are many drugs that have an effect on the body, but no effect on the brain due to the blood brain barrier), i.e. the body is complex.
That said, it's generally recognized as safe and may potentially cause side effects in some people but there isn't much evidence for it, and MSG is one of the most studied food additives in the world.