The two pieces of the question do not fit together. The "religious group comprises a majority of Iraqi population" was the Twelver Shiite Muslims and the "religious group that held political authority and economic power under the Saddam Hussein" was the Sunni Muslims. The Sunnis were an empowered minority while the Shiites were a powerless majority.
Afghanistan is 99% Muslim with 80 to 85% following the Sunni sect.
the religious group were the puritans
A majority of Chinese belongs to the Han ethnic group.
Only that your demographic group (whatever it may be - racial/religious/ethnic/etc) is numerically smaller than the prevailing majority of the population.
The pluralistic with many industrial, cultural, economic, educational, ethnic, and religious groups are belongs to the interest group.
moral majority
A population group refers to the group to which an individual belongs. An example of a population group is Arab, Chinese, Filipino, Latin American, or White.
I don't think they hate atheist. It's more like distrust. People have a tendency to distrust someone who you considered an outsider of your own group. This is why that it's unlikely that a U.S. politician will claim that he or she is not part of any religious group because the majority of the U.S. belongs to some religious group, whether they are active members or not is another issue.
The majority of the Mayflower's passengers on the journey to Virginia were Puritans, a group who believed that both the Church of England and the Catholic Church in England had strayed from the teachings of the Bible.
Hispanic
Hinduism is the by far the dominant religious group. Hindus constitute more than 80% of the Indian population.