Gynecologist is demanding pap smear in order to get BCP, what can I do?

Long story short. I have been having irregular periods. Physician recommends I ask a OB for birth control pills to regulate them. I go to OB, a new one, and tell her what's been happening. OB basically tells me to strip so she can give me a pelvic exam and a pap smear. I tell her that I already got a pap smear last year with another OB (switched to this new one after moving). OB says that they are required or she won't prescribe. I tell her that the AMA recommends pap smears at my age only once every five years, she tells me that they are wrong and it should be annually.

Did not get prescription.

What do I do now? Will this be an issue with every OB I go to? Even the other OB I had previously would basically hold the BCP hostage unless I did a pelvic and pap smear. People tell me to just quote the AMA but it never seems to work. I don't even live in the south or somewhere conservative, I live in New Jersey.