At one point, I tried two different manufacturer's radials on one of my bikes designed for radials, & equipped w/them from the factory, one of the very-1st Jap. bikes so-equipped. One mfr. in the front, another mfr.'s in the rear.
There are different angles of construction for the warp plies of the tire in a radial construction. Some are a "V" of varying angles, some are where alternating layers are at right-angles to one-another. I cannot recall which tires they were, or which angles, but I do recall what it did to the handling. It ruined the handling! I kept them like that for 1000 miles, and then bought a second front matched to the rear. I can't recall why I went that way, to begin-with, it probably was related to tire pricing and my funds at the time. Never-again!
Yes, some bikes have had bias & radials, I think H-D had some like that. Unless you replaced the tires on a bike which came that-way, I would never recommend anyone do that. Nor would I ever recommend anyone go 'Dark-Side,' car tires in-place of a mcy tire, unless you are running a sidecar, and it cannot lean.
Our bikes have suspect handling in the minds of many, why throw another detrimental factor into the mix? Use a matched pair for safe and predictable results, and radials are your best bet. A Kosman remanufactured wheel is about $550, check w/them for current pricing, and a pair of radials shoud run you about $250 on-sale. Spoon 'em on yourself, and static-balance them, and you have radials on a budget for ~$800+. You send Kosman your rear wheel & they send you back a modded wheel. Re-use the front wheel, and buy a sensible-sized front tire (NO 120's!), and be-prepared to experience vastly-improved handling compared to what you are used-to in riding the 'Max!
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