I've mixed brands on some bikes when it was necessary with no ill effects. Sometimes it is because one manufacturer doesn't make the model tire I want in the size I need - especially for bikes like my Kawasaki Concours, which has a 17" front wheel. I do avoid mixing radial and bias play tires though - either both radial or both bias ply - that's how I roll.
I do try to get tires of the same/similar speed ratings, so that they wear a little more evenly and my traction/cornering angle is more consistent across various road conditions and speeds. sometimes the lower speed rated tires with harder, heavier rubber will grip on gravel roads better, but the high speed rubber will grip on wet asphalt better. I don't want the front or back end sliding out prematurely!