Can I replace 205 tires with 215 tires on the rear of my 2000 GMC Sonoma pickup

If it's a wider tire you want then it shouldn't be a problem the rim should accept that ,, I don' t think that truck is so high tech that a higher tire would matter , 205 /215 is the tread width in milli meters , the 70/75 etc. is the % of that # in height , If you think a fatter tire is better traction in snow I think that's not true .

I'm just trying to find out if it would cause transmission problems

I don't think it would cause tranny problems or with the computer , A 205-75 would be as high as a 215 -70 , Even if you wanted the height too it shouldn't be a problem .