Is it permissible to pray behind someone affiliated with a non-Islamic party—such as the Ba'ath Party—or a non-Sunni, and is it permissible to declare the common Shiites as disbelievers?

The general rule is that prayer behind anyone who attributes himself to Islam is valid, as long as he has not apostatized from the religion. However, if a person's disbelief is established, then prayer behind him is not valid. It is preferable to avoid praying behind a transgressor (fasiq) and those who hold grave innovations (bid'ah). The statements of the common Rafidah (Shi'a) are indeed statements of disbelief (kufr), but a specific individual among them is not declared a disbeliever until proof (hujjah) has been established against him. This is because a statement can be disbelief, but the specific person who uttered it is not judged to be a disbeliever until the proof is established against him. Therefore, avoiding prayer behind such individuals is what should be done.