When the dentist applies the rubber dam on you, is it normal that it makes you want to gag?

Yes: Yes very common, more for the back than front teeth. You may ask your dentist to prescribe a sedative like valium to help.

Unfortunately yes: Everyone's gag reflex is different and most dental offices try and deal with it the best they can... Some have the patient rinse with mouthwashes prior to treatment, some use sprays, others use distraction. Sometimes the patient has his/her mind set that they are a gagger, and that's what they do.