If I use a credit card to buy tickets, they can already track what I'm watching. And that's not even mentioning MAC address tracking that some places do.
I believe there are laws against using credit cards for the purpose of ID'ing and tracking customers. I don't know if they're state (I'm in CA, where consumer rights are stronger) or federal.
Do the theaters share purchasing information with studios or others? I would think that in the age of privacy policies, they would have to tell you if they want to do this.
I think I'm thinking of the Song-Beverly Act, which is a CA law, though reading this synopsis [1], I'm not sure if they can't use the cc number to track you, or if they just can't require you to give other PII in the cc transaction. In some cases this might amount to the same prohibition. But again, it would only apply to CA consumers (defined either by residency or by current location, presumably, which further complicates things).
> The Song-Beverly Act prohibits retailers from requiring a consumer to provide personally identifiable information (PII) as a condition to payment by credit card and recording that information during the credit card transaction. The Act defines PII as including the cardholder’s address and telephone number, and courts have repeatedly found that the definition includes other information such as ZIP codes and email addresses. Class actions against retailers in California based on alleged violations of the Act have become commonplace and several other states have also adopted their own laws modeled on Song-Beverly.
