Saw old movie where after sex they get itchy and break out in hives all over. what could this be?

Sci Fi Plot: Some women, and this is very rare, develop allergy antibodies to male semen resulting in anaphylaxis during or after intercourse. One symptom of anaphylaxis is hives. But you referred to "they". There are only 2 things that can give a man hives during intercourse - latex allergy if he is using a latex condom or exercise-induced urticaria. Don't lose too much sleep over these possibilities.