As Don writes, Bill Walsh used more white players than many of his contemporaries. Dwight Clark made one of the all-time great catches ("I didn't know a white man could jump that high," a black Cowboy said) from Joe Montana to beat Dallas in the 1981 NFC Title game.
Also, Walsh was one of the last coaches to use a white runner as his main RB. This was Paul Hofer during 1979-80. Walsh had Hofer receiving as well as running, often complex patterns, not just dump-offs. I recall a comment by Walsh on Hofer's lack of recognition. He said something like, "Paul doesn't get much credit because of what people think about white running backs. He's the key to our offense."
Unfortunately, Hofer tore up a knee in the sixth game of the 1980 season. He had 760 yards combined rushing and receiving (source: Total Football) at that point. Hofer tried to come back the next year, but was injured again, and missed the playoffs. He had to retire. During 1978-80, after Walter Payton and Earl Campbell, Hofer played as well as any RB in the NFL.