Avon says:
TIRES: RADIAL VERSUS BIAS
While running a bias ply front tire and a radial rear tire can be acceptable in certain applications, you should never run radial front and bias rear as this can create an instability issue.
And Dunlop:
Above all, do not mix bias ply and radial tires on the same motorcycle unless it is with the approval of the motorcycle or tire manufacturer.
And Motorcycle USA Magazine:
Don't Mix and Match Bias and Radial Tires
Bias and radial tires have significantly different dynamic properties. Bias, bias belted and radial tires have different construction types and therefore have different abilities to carry side and peripheral forces as well as having varied damping characteristics. The introduction of radial tires required changes to certain characteristics of the motorcycle. The development of the radial tire led to frame modifications, new steering geometries and suspensions. That's why it is recommended that a motorcycle be used with the type of tire construction that it came with originally. Do not mix bias ply and radial tires on the same motorcycle unless it has the approval of the motorcycle or tire manufacturer.
Everything I ever read said Never use a Radial front with a BIAS rear.