Look at it this way, if differences in tire compound are going to show up it's not giong to be doing 30 taking grandma to church now is it?
No, it's gonna be that corner that you don't care if it's wet because you've taken it a thousand times and know exactly what the car can do.
Whoops. You knew what the car could do with four tires exactly the same and now the fact that your back end is now leading the way and you're following in the front cabin suggests different tires behave differently and there are times when this matters.
So can you mix different tires? Depends how you drive. My dad gets away with it. I won't even try any more.
To be sure there are tires you can "match" that act pretty similarly but then again there are random combinations, mostly differing in when the tire breaks away, that are bordering on downright lethal and that can be said of even different tires within a given manufacturor.