Different brands shouldnt be a problem at all. I've had different brands and patterns on all my bikes. Currently my KTM (640 Adventure) has a Dunlop 606 front and Mitas E07 rear.
I choose different brands and patterns based upon the performance and life I want. Im happy to accept a shorter life for better grip in the front and longer life with less grip on the rear. Thats just my preference.
Edit: Adventure riding is a mix of on and off road. I have a road biased rear which lasts longer but has less grip on gravel/dirt/clay.
On a road bike I would say it would make sense that they are a similar type so they have comparible levels of grip in the wet.
More importantly as the owner/rider you need to be comfortable and familiar with how the tyres behave in different conditions.
Unless you're riding at the extreme limit of your tyres (ie racing) I doubt brands will make any difference at all.
Matching tyres on a car are more significant because under severe braking different brand/patterns with different levels if grip can make the car pull left or right. On a bike that is not a consideration.
To illustrate the counter point with a ridiculous extreme: you could have completely mismatched tyres from the same manufacturer. Would the brand matter?
To reiterate my point. You need the right TYPE of tyre for your bike and the riding you do, that suits your riding style and preferences.
If you put an expensive high performance tyre on one end and cheap rubbish on the other and have an accident. Dont blame the brand. Blame your self for expecting cheap rubbish tyres to behave like a high performance tyre.