Are the words christian, buddhist, hindu, and muslim proper nouns?
Christian, Buddhist, Hindu, Muslim
They are proper nouns because they are specific (referring to one believers of a religion by a name, rather than a general word such as religion which doesn't specify a religion). They must be capitalized.
Other examples of proper nouns:
Tokyo (names of cities)
Arkansas (names of states)
Zhejiang (names of provinces)
Canada (names of countries)
Oceania (names of regions)
Francis Crick (names of people)
Zoroastrianism (names of religions)
Proper nouns is to be specific.
Note: There is a difference between proper nouns and commons.
Ex: I am from the Middle East. << This is common. Because you are not being specific - there are a lot of countries in the Middle East.
Ex: I am from France. This is proper noun. Because you are being specific about what country you are from.
Christian, Buddhist, Hindu, and Muslim
I don't think I would consider Christian as a proper noun because there are different groups of Christianity.
For example, you have Catholic, Jehovah's Witnesses etc...they all considered as Christian.