My project bike has a brand-new Dunlop D220 on the rear, and a worn out Dunlop 207ZR on the front.

From what I've ready, everyone hates Dunlops...

And strangely enough, Michelen Pilot Powers (which everyone loves) are slightly cheaper.

Is mixing up brands and compounds a bad idea? (ie, sports touring rear and a supersport front)

The fronts are a bit dry-rotted, but I'd say I'd at least get a few miles out of them with the tread that is left (has a few MM of tread).

 

It is a bad idea to mix brands because of different contours in the tire.

Find out if you can sell the rear to somebody, or if the shop will give you $100 for it or something and get 2 new tires.

OR, if you dont ride very hard, dont worry about it.

 

I'm not sure if it's the contours as much as differences in the compound and how they stick to the road. Brands are matched for hardness/softness as well as tread pattern. (plus the front pattern is backwards from the rear anyway because of forces exerted on the tire.) if the tire is a bit dry rotted I would replace it even if it still has tread left. I put a Michelin on the rear of my bike and the bike handled and rode great with the Dunlop on the front, but it was starting to get the cracks, so I replaced it with a matching Michelin. (to the back) the ride is a bit harsher, but they are both newer tires and of the same brand line.

 

It's more about tire profile than "compunds".Onstreet tires,there really isn't much difference in the compounds in street sportbike tires,even though some will argue that as well.
If you have different profiles on front and rear (pointy vs. rounded),youhave two tires rolling on different arcs.That can get scary,quick.