Looking at running the BMC GT500 style rims in a staggered setup on my 2015 GT. 20x9 +25 up front & 20x10 +37 out back. Wanting to know if I could run 305/35r20 in the back with no problem and a 275/35r20 up front
That's too big to run on a 10 in rim imo, not that it can't be done, just wise not to. Back it down to a 295 max, though 285 would be better imo. If you want to run a 305 you may want to consider an 11" wheel.
Should be okay in the front. Again I'm just talking tire size not offset. So someone else will want to chime in for that.
Are you more set on those wheels or running those tires? Either one on their own will work, but when paired together it is far from ideal. Why are you trying to cram such wide tires on those narrow (in comparison) wheels?
If you want those wheels, offset wise they will fit with the proper tires on them. They will likely rub for sure in the rear without a lot of negative camber when trying to run a 305 on it. 255/35-20 front and 285/35-20 rear would be perfect.
If you want to run those tire sizes, you should get 19x10" front and 19x11" rear wheels. As for offsets we produce our 10" with a +40mm and the 11" with a +52mm.