According to "Multiple chemical sensitivities: A systematic review of provocation studies" (Journal of Allergy and Clinical Immunology 2006)[1], perfume sensitivity is largely psycho-somatic. This means that we experience symptoms because we stress about the perfume exposure. Since learning this, I have employed stress-management techniques during perfume exposure and have enjoyed 90% reduction in symptoms.
What I've noticed anecdotally (feel free to critique this) is that of the few people I know who appear to fit that profile of having MCS, it's of my opinion that they would all benefit from stress-management techniques (including outdoor cardio exercise to help with breathing). I would suggest it to them if it weren't for the fact they're merely acquaintenances and not friends.
Of course, I don't mean to suggest that obnoxious use of perfumes should be encouraged, but for those who are extremely sensitive, it's perhaps worth a look given how rarely doctors seem to seriously prescribe exercise (I think part of the reason is that taking up a new form of exercise is intimidating and difficult to monitor for many people, and that not all doctors live the healthiest of lifestyles themselves).
[1] https://www.ncbi.nlm.nih.gov/pubmed/17137865