If one rides pretty much straight up and down, mixing manufacturers shouldn't be an issue. If one is mixing bias and radial, the bias would be best on the front and the radial rear.
However, if one is a fairly aggressive rider and actually activates the sidewall of the tires when cornering, the best approach is a matched set of tires from the same manufacturer. The last thing one wants when riding aggressively if to have the front end acting one way and the rear end another, which will happen if the tire combination is bias/radial and is likely to happen if both tires are bias or radial but from different manufacturers.
So, if one is dragging stuff when cornering, particularly if trail braking and a lot of lean angle is being used, best to run a matched set of tires; same manufacturer and same construction.:s
Look at your rear tire; if the wear is predominantly in the center of the tire, there will be "chicken strips" of no wear on from the edge of the center out on to the sidewall. If this is the case, don't worry too much about running a matched set of tires. However, if there are no "chicken strips" or very narrow ones, that means the sidewall is being activated in cornering and it becomes more important to run a matched set of tires.:coffee