If you're going to mix tires, at least see that:
- the tire construction is the same
- the tread compound rubber 'hardness' is similar
Radials have one method of construction where top layers of cord are perpendicular to the underlying circumferential layers (zero-degree)and another where they are at oblique angles to each other (less than 90*). Choose one or the other.
As for hardness, having a sticky front and a hard rear can cause your rear end to break loose when you least can afford to, like in a curve. The front 'sticks,' you feel confident, and you crank in some power, and then the rear, losing traction, breaks-loose. The opposite would probably not be as-risky, but I prefer to have confidence in my tires, and you get that from buying the same brand/style of riding tires.
I once experimented w/different manufacturer tires front and rear (two different brands) on my FZR1000, one of the first stock bikes to run radials. I don't recall the tires or the type, buy the handling and my confidence in it went completely away to the point where I replaced the front tire in < 1K miles. It was scary, I had no confidence in the handling, and every time I tried to ride it like I had been, in curves, it just was horrible. No it wasn't some cheapo tire, just a really-bad match.