I think that in many cases the halfbreed functioned like the bounty killer - his ambiguous/outcast status vis-a-vis conventional Western archetypes was of great interest to the more ideologically minded/iconoclastic Euro-Western film-makers. He enabled many artists to make their politcal/anti-racist points more forcefully, while even those who weren't ideologically minded preferred outcasts and mxed-race characters to more straightforward hero figures, often with the same effect. (I'm thinking principally of escapist films such as My Name is Pecos and Vengeance here.)
Of course, a great many films simply followed the lead of the more thoughtful examples.
This can all be taken with a pinch of salt, but I don't think the large number of halfbreed antiheroes is merely coincidence.
Very true also, and reflected most famously in Clint Eastwood's mixture of American/Mexican attire in the Dollars movies. When they got it right, the 'melting-pot' milieu was one of the Euro-Western's greatest strengths.