In fact, it's an Indian who first brings Chris (Yul Brynner) and Vin (Steve McQueen) together to form the group's nucleus. Unfortunately, he's a dead Indian who's been lying in the street two days. Here's the undertaker (Whit Bissell) explaining the situation to Henry and another salesman:
Salesman: What? In Boot Hill?!
Henry: There's nothing up there but murders, cutthroats and derelict old barflies, and if they ever felt exclusive, brother they're past it now.
Undertaker: They happen to be white, friend. And old Sam ... old Sam was an Indian.
Henry: Well I'll be damned. I never knew you had to be anything but a corpse to get into Boot Hill. How long's this been going on?
Undertaker: Since the town got `civilized`. Oh it's not my doing, boys, I don't like it, no sir. I've always treated every man the same, just as another future customer.
We don't know if Chris and Vin harbor other prejudices, but their willingness to stick up for an Indian is telling. Clearly, they have the stuff of heroes inside them. It's no surprise when they decide to protect a poor Mexican town for the principle of it.
Judging by the town's festival, the farmers' culture has a strong Indian influence. Their celebration is a mixture of Catholic and Native religion (e.g., a dancer wearing a deer's head). You can see similar celebrations in New Mexico's pueblos today.
Also, the Harry Luck character keeps speculating about what the seven are really protecting: gold, silver, gemstones, etc. Eventually he suggests it must be "Aztec treasure." It's a further confirmation that the region has Indian roots.
For more on the subject, see The Best Indian Movies.