If you fire the person with the allergies you have opened yourself up to a serious lawsuit. While a big company may have the attitude of "regargless of the cost" I don't think that the average company could afford that, not to mention the bad press that would result for that type of suit.
You forgot on little thing. Most companies have “at will” employment clauses. I can and have let people go for these reasons, with no legal recourse on their part. You should read the application you filled out. That clause has to be read and signed before you become employed with the company.