The question is to prove there were movies made about white families helping african americans and it is really helping life today.
The film Mississippi Burning comes to mind, and although not with specific white families it is based on the murdered college students (two of them white) who went to Mississippi to register African Americans to vote in 1964. The film does not portray 'historical truth' but I do believe it delievers 'truth of emotion'. In reality F.B.I. Director J. Edgar Hoover was no civil rights champion, however the media attention Jessup Mississippi recieved in 1964 ultimately had a powerful effect on many Americans of every color across this country. Since I was only six in 1964 I asked my mother if she remembered seeing this event on the news in New York City...she remembered it. Andrew Goodman, Michael Schwerner, and James Chaney believed in what they were doing for those disenfranchised Americans in Mississippi and paid the ultimate price for those beliefs.
One movie that comes to mind is The Long Walk Home,directed by Richard Pearce, and starring Sissy Spacek and Whoopi Goldberg. Whoopi Goldberg plays Sissy Spacek's maid. The movie takes place during the Montgomery, Alababma bus boycott in 1955, which was when the Civil Rights movement was just getting started. At that time, African-Americans were only permittted to sit in the back of the bus, and you might have already learned that Rosa Parks set things off by refusing one day to move from the front section of the bus. This boycott led to the United States Supreme Court striking down segregated public transportation.
I hope this helps. Good luck to you!
Two movies that I think of immediately are A Time to Kill and Remember the Titans. The first is the film version of John Grisham's novel of the same name, and the second is based on a true story. Neither movie focuses primarily on a white family helping an African American family during the turmoil of the civil rights movement, but this storyline does play a very important part in both movies. The white characters in both movies are condemned, shunned, and even physically threatened because they choose to reject racism and follow their hearts and consciences. Both movies, with their themes of decency and brotherhood, were--and continue to be--very popular.
This is a miniseries more than a movie, but did you try Roots: The Next Generation? I can't remember specifics, but after reading the novelization of Roots and then watching that miniseries, it is obvious that "good" white characters were inserted into the movie version so as not to anger the white audience in the majority. I have a feeling that the same would be true about the second installment.
If you are looking for another sports film, "Glory Road" might be something to examine. The story is about Clem Haskins and his UTEP team of predominantly African Americans winning the NCAA Basketball Tournament by beating the all white team from Kentucky and Adolph Rupp. It is a great story of Haskins and his family (but more Haskins) supporting young African American men in the 1960's.
Several years ago there was a movie called, The Color of Friendship. It was set in South Africa and it addressed apartheid. I believe a white girl was staying with a black family, and even though the father was politically significant others still caused a problem for the two girls.
A couple that come to mind but not quite sure they match your criteria are The Rosa Parks Story and Ruby Bridges, they are from 1998 and 2002. An older movie, from 1964 titled Nothing But a Man might also be worth checking out.