Different tires - front and back?

Hello
I think this will not be a problem. Of course, this is not desirable, and in the coming year you better fix the situation by ordering the same kit. But for my Prius, too, had to purchase tires of different production

 

The main thing is to take good quality tires. In case of difference in their sizes, choose from trusted manufacturers, do not save on such for example

 

As Mike Focke said, you do not want to confuse the ABS (or VSC, or wheel slip logic) with the tires on one axle spinning at a different rate than the other. What the logic trigger limit % differential, and thus the tire diameter % differential, limit may be is anyone's guess.