The main problem is that over time you become more and more sensitive to it. So even if initially you have no response don't be surprised if after some time of using it regularly you have really bad allergic reactions to even mild exposure.
Yup. Anecdotal story, a friend of my father was making a boat for himself and he became so sensitized to epoxy that he had to stop working on it and hire somebody else to finish it for him.
(For boatbuilding, the usual choice is polyester resin rather than epoxy, which is nasty in other ways. You don't wanna be inhaling those styrene vapors all day long.)
I'm no professional boatbuilder, but I've been helping out friends and family with DIY glassfiber boat repairs and improvements. So yes, I have experience of both polyester resin and epoxy. They have their own issues, as discussed in this thread.
Epoxy is highly allergenic (or whatever the word is), so you should be pretty careful about using nitrile gloves or similar when working with it. Personally I don't find the smell particularly bad, and it's not very strong, at least compared to polyester resin.
Polyester, yes it smells bad, and as I mentioned in my parent comment that's styrene vapors you're inhaling, which is a known carcinogen. If I were to do some bigger job with polyester, I'd definitely want some pretty hefty breathing filter. But for the occasional one-off thing, particularly if you can do it outdoors, meh..
Mostly a gut feeling: Anything someone can grow sensitive to, such as this or smoke or anything, should at least be very carefully examined as a cause of harm generally.
That's partly about concentration. I've heard of people becoming allergic to lavender, which is normally pretty unlikely, because they imprudently used the concentrated oil on their skin.
AFAIK most allergies/hypersensitives are for harmless things; animals, pollen, and different types of food. So basing what we grow sensitive to might not be the best test to see if a product can cause harm
If you get resin on your skin and it starts curing under your skin your immune system will have to get rid of the stuff under your skin and because it is so difficult to get rid of cured resins your immune response will be incredibly sensitive.