What is the finish that comes pre-applied on the proofgrade plywood and veneers?
It seems nice–and also really hard to remove. I need to glue two pieces together and it’s difficult to sand down to expose the wood itself. Is there a glue that will work well on whatever this finish is?
Several work really well. 
First step is to use some 60 grit to scratch it - you don’t have to remove the finish completely, just cut some grooves into it.
Then depending on the time I’m willing to wait:
Gorilla white wood glue with clamping.
Any cyanoacrylate glue. (Superglue).
Any kind of contact adhesive.
The wood will break before the glue does.
I tried a few things and found that a brush-on satin polyurethane finish produced a result very similar to what you see on Proofgrade plywood.
Weldbond is also great glue for multi-surface stuff. I use it often as a slightly-flexible dries-clear wood glue. It’s PVA so you’ll want to test it on the prefinished surface, but it seems to bond certain things better than other PVA wood glues do.