Mix and match tire brands

I need a new rear tire, is there any reason not to get one that doesn’t match my front Avon? Any issues with compatibility?

No issues at all as long as both tyres grip the road good.

I rode a 6,000 mile loop from Tennessee to the INOA Rally, SoCal, and back last summer with an Avon RoadRider on the rear and a Shinko 712 on the front. The tires were on the bike when I bought it shortly before setting out, and saw no pressing reason to replace a good tire. I rode fully loaded with gear in all kinds of weather including heavy rain, desert heat, and cold rain crossing the Rockies without any tire problems. The Shinko still has plenty of life left, but I replaced the rear with a Bridgestone 120/90-18 when I returned home. If there is an issue, I have no idea what it is. Some will disagree, and that's fine.

Shinko 712 for the win.

Depends and I don't mean the man diapers. I have a Continental Conti-Go 100/90-18 on the front and a Bridgestone Battlax BT46 110/80-18 on the rear. The Bridgestone on the rear does not like metal grated bridges. It makes the rear feel like it is completely flat and wiggles all over the place. Otherwise it's fine I think. It might act a little funny on Highway rain grooves, but can't remember. With Conti-Go tires front and rear the bike was good on any surface, but dirt. Front tires last a long time on my Norton. Rears don't last long.