The simple answer to this question: yes.
It turns out, the term hypoallergenic probably doesn’t mean what you’ve been assuming it means all these years. According to information found via the Government of Canada’s website re: consumer products and cosmetics,”hypoallergenic is neither a legal or scientific term” and really only means that the manufacturer has placed ingredients into the final product that are less likely to cause an allergy or reaction to occur.
Now, this needs to be clearly stated: “less like to cause a reaction” doesn’t meant that you’re free from the possibility of developing a reaction to an ingredient within a formula marked hypoallergenic.
Everyone is different and, as such, can be allergic or have a reaction to a range of substances, no matter what form they take: natural, synthetic, “hypoallergenic” or otherwise. The website also states “there are no non-allergenic cosmetics”.
So, what does that mean for you and your cosmetics shopping experience? If you find yourself with extremely sensitive skin or reacting to multiple products on a daily basis, consider a trip to a dermatologist to ask for help in diagnosing or recommending alternatives for your situation. Outside of this, if you are reacting to your cosmetics, try isolating the problem and doing patch tests on your arm so you can figure out which product(s) is/are causing the irritation.