Movies with a blonde-brunette rivalry.

2 Days in the Valley (1996) - Charlize Theron vs. Teri Hatcher

Rowena (the blonde) and Rebecca (the brunette) in "Ivanhoe".
They don't really interact with each other much, but they still are in a love triangle with Ivanhoe.
And in the 1982 version at least, Ivanhoe himself and Brian Guilbert also qualify.
Ivanhoe is blonde and Brian Guilbert is dark-haired.

Meet The Parents (2000) - Ben Stiller and Owen Wilson’s characters
Seven Years in Tibet (1997) - Brad Pitt and David Thewlis’ characters
All The President’s Men (1976) - Woodward and Bernstein started off as rivals until Bradley put them both on the story.

Rocky IV (1985)

True Lies, Mischief, Teen Wolf, Secret Admirer

Underworld (2003) Selene & Erika

Showgirls

Gone Girl. Maybe not the intention of the OP, the identity switch provokes some thoughts.

Also Mulholland Drive. There is more going on in that movie than I'm prepared to address, but it's pretty B&W concerning the topic here.