Iraq was pretty diverse. And they remained even so even after centuries of Islamic rules. Iranic rule by the Parthians and Sassanid had little impact on the local demographics too.

The main ethnicity in western and southern Iraq was pre-Islamic Arab tribes, ruled by the Lakhmids tribe, as a vassal state the Sassanids. These people were Eastern Christians, or at least their elites were. As their branch of Christianity was different from the Christianity of Eastern Roman empire, they are not friendly to them and proved to be useful ally for the Sassanids, Roman's greatest enemy. The Lakhmids were also useful in keeping various nomadic Arabs from the desert in check. That is, until the Sassanids turned on them and killed their king Numan. This caused the Lakhmids to ally with their fellow Arabs from Mecca and helped them conquered Persia.

The northern Iraq was inhabited various people like Assyrians (who are also Eastern Christians), Aramaic-speaking Mandaean (who have their own pre-Christians religion), while the mountainous region was inhabited by various Iranic people, like the Kurds.

Ctesiphon, located in central Iraq near where Baghdad is now, was the capital of Sassanid empire. There are plenty of Persians here, apart from local peoples. Additionally the city was populated by various ethnicity of Sassanid empire, as it was first populated by Khosrau I using deported people from across his territory. The result was that this capital was a highly diverse city. Ctesiphon was the "center of Eastern Christianity", as the leader of the Church of the East was located here. It was also home to significant population of Jews.