No, a credit card application shouldn't be rejected due to political beliefs. In fact, none of the major credit card companies ask for information about your political beliefs during their application process.
Fair lending laws ensure that creditors provide unbiased treatment to all customers. So, issuers cannot reject your application because of your race, color, religion, national origin, gender, marital status, age, or because you receive public assistance, either. The law guarantees the same lending opportunities to everyone.