Latex allergy question

Most house paint has latex as an ingredient. Is this a problem for people with latex allergies? I’m kind of figuring that if the paint is dry, it probably isn’t (you could put your hand on the wall with no problem?), but what if it’s wet? Would touching wet paint be a problem? What about breathing the fumes–what if you went into a house where someone was painting a room? Do you just have to pay other people to paint your house?