It wasn't common. Re: Miss America, the only one I found was Vanessa Williams back in 1983.
In 1970, however,
Cheryl Browne,
Miss Iowa 1970,[SUP]
[23][/SUP][SUP]
[24][/SUP][SUP]
[25][/SUP] competed as the first African-American contestant in the
Miss America 1971 pageant.[SUP]
[26][/SUP][SUP]
[27][/SUP][SUP]
[28][/SUP] She also participated in one of the last
USO-Miss America tours in
Vietnam.[SUP]
[27][/SUP] A decade later in 1983,
Miss New York (and Miss Syracuse) 1983,
Vanessa Williams (the first
African-American woman to win the competition as
Miss America 1984), faced discrimination in response to her win and later resigned under pressure due to a scandal involving nude photographs.[SUP]
[29][/SUP][SUP]
[30][/SUP] Three decades after these events,
Miss New York (and Miss Syracuse) 2013,
Nina Davuluri, the first
Indian-American woman to win the crown as
Miss America 2014, faced
xenophobic and
racist comments in social media when she won.[SUP]
[29][/SUP][SUP]
[30][/SUP] Two years later at the
Miss America 2016 pageant, former Miss America CEO Sam Haskell apologized to Vanessa Williams (who was serving as head judge) for what was said to her during the events of 1984.[SUP]
[31][/SUP][SUP]
[32][/SUP][SUP]
[33][/SUP]