User ihatepattycake claims the answer is yes. Your very presence is probably making a few unfortunate kitties suffer. "In my practice we regularly perform allergy testing on dogs and cats. One of the allergens we test is human dander. Thankfully, we don't see a very high incidence of positive results (5-10%) compared to other allergens. However, when we do get a positive reading it normally comes as quite a surprise to mom and/or dad." Yikes!
What the heck is human dander, you ask? Well, much the way animal dander consists of flakes of skin and oil, so does ours. (If you've ever really looked at a dust bunny, you know what we're talking about.) And though it's not totally clear what components of human dander can cause adverse reactions in cats (or dogs), it's not all bad news for animal-lovers. If your cat is actually allergic to humans/you, you can simply give it antihistamines.
Interestingly, cats can't be "allergic" to themselves (we looked into it), because by definition, an allergy is strictly an immune response to a foreign substance; anything else would qualify as an autoimmune response, which is scarier.
Thanks, as always, to Reddit, for enhancing our Saturday night with this #TheMoreYouKnow moment. (Reddit)