Matthew Richer's article Like Father, Like Son—Betraying The GOP Base Is A Romney Family Tradition goes into detail about the record of George Romney, father of Mitt, and Governor of Michigan in the 1960s. I've found more material:
"Peter Luke, a columnist with the Ann Arbor News, noted that "More than 30 years ago, when other leaders were unwilling to confront virulent racism not only in the South, but in their own Northern back yards, George Romney did just that." This made his tenure as governor "one of Michigan's proudest moments."
Judge Damon Keith, [who is black]who was appointed to the state's new Civil Rights Commission under Romney and now a senior judge on the U.S. Court of Appeals, said that "Gov. Romney always took positions of integrity and conscience. That's the way he lived his life."
George Romney: Rock-Solid Character And Heart Of Gold Showed In Every Facet Of 'Citizen's' Life. By Hal Knight,deseretnews.com, August 20 1995
The Chicago Reader pointed out this one:
"Civil rights for African-Americans was George Romney’s lifelong, passionate cause, undertaken in defiance of his church as well as the conservative wing of his party; Mitt has shown scant inclination to follow his father’s example."
Romney vs. Romney (Review ‘The Real Romney,’ by Michael Kranish and Scott Helman)By Geoffrey Kabaservice, NYT Book Review, April 13, 2012
The Chicago Reader also writes
On racial desegregation, the elder Romney was more liberal than most Democrats are today. He realized that attacking segregation required targeting discriminatory government policies that trapped blacks in city ghettos. Since cities were crowded, it meant, in particular, opening the suburbs to blacks. As HUD secretary, he was outspoken on the need for desegregation. "The most explosive threat to our nation is the confrontation between the poor and the minority groups who are concentrated in the central cities, and the middle-income and affluent who live in the surrounding and separate communities," he told an association of home builders in 1970. "This confrontation is divisive. It is explosive. It must be resolved."[George, Mitt, and HUD Posted by Steve Bogira, May 17, 2012]
Mitt Romney reported in 2007 that he cried when he heard of the 1978 ruling that made blacks eligible for the Mormon priesthood:
"I can remember when, when I heard about the change being made. I was driving home from, I think, it was law school, but I was driving home, going through the Fresh Pond rotary in Cambridge, Massachusetts. I heard it on the radio, and I pulled over and, and literally wept. Even at this day it's emotional, and so it's very deep and fundamental in my, in my life and my most core beliefs that all people are children of God." [Meet the Press, December 16, 2007]
After reading Richer's article, I can attribute this to the influence of Mitt Romney's father as well as his religion.
Remember that George Romney was Governor of Michigan when blacks burned down large parts of Detroit, and reacted by going on a 17-city "ghetto tour" to ask blacks what whites were doing wrong. See No Politics,'Catfish' Tells Romney On Slum Tour, By Larry Hatfield, The Pittsburgh Press, September 12, 1967