You CAN mix and match and my home is the PERFECT example! lol
We've got: an American Bulldog (outside); a Staffordshire Bull Terrier (inside/outside); a Black Russian Terrier (inside) and a Yorkshire Terrier (inside). Everyone mingles from time to time except the Staffie and the AB, they'd kill each other if they could. Otherwise, no issues.
I think it all depends on how you pick on their manners when they're around other dogs and that's pretty much it. A lot of owners don't know how to handle a multiple dog household, let alone a multiple breed household and I think that's where the steriotype comes from that it can't be done...not safely anyway. And I'm here to tell you they're wrong.
Also, I'd like to mention that my folks have a multiple dog and breed household as well! (Akitas/Yorkshire Terrier)
It's fun, and wonderful to have the breeds you love and can care for properly!