Capitalize names of languages, nationalities, ethnicities, political parties, religions, and religious denominations. Do not capitalize political doctrines (conservative, progressive). Do not capitalize white or black as a designation of race.
an Arab man
the Catholic Church (but: a Methodist church, First Methodist Church)
Indian American community
of Italian heritage
Although she has been a member of the Republican party for years, at one time she was a Democrat.
This legislation endorses the principles of democracy in our republican form of government.