I've run bias plies & radials mixed both ways front & back. The only time I had the back end wagging on the big end was entirely due to bias-plies on the rear being run w/ too little air.

FWIW, when I run radials up front at the track I set 'em at 40-45 psi to keep the sidewall flex down. When I paired them up w/ bias-ply rear tires on the street, I also ran them that high to keep the car's handling better balanced.