The differing handling characteristics will often result in dangerous and unpredictable vehicle behavior - especially in emergency situations.
Back in the day when radials were first introduced to the US, some folks tried mixing them with existing bias ply rubber with some ugly results.
So if you plan to drive only on dry pavement and never over 30 mph, perhaps it will work for you. Otherwise, either replace your rear RFTs with the same tire as the fronts (RE 050A?), or buy 4 go-flats and sell your existing front tires to recoup some of the money.
My dealer is happy to mount and balance tires, but they will not mount non-RFTs, however Tire Rack will provide a list of recommended installers in your area.