Ok, now I'm confused. I've been reading previous posts concerning wheel offset and tire size trying to find an answer to my question.

On a stock height MINI S, will a 7 x 17 wheel with an offset of 40et mounted with 215/45/17 tires cause a rubbing problem? If so, will spacers solve the rubbing problem?

 

I have almost the exact same question, but the specs are just a little different.

2007 R56 MCS, 17x7, 42mm offset, 215/45 17 Michelin Pilot Exalto PE2. However, I'm not interested in using spacers. If these would rub, I'd go to 205/45 17.

 

Your stock suspension MINI will be able to use a 17x7 rim with about +38 to +48mm offset and 215/45-17 tires without significant rubbing. The greater the offset the more likely there will be enough clearance. +40 should work ok. The exception can come with other factors:
Big brake kit with oversized calipers.
Aftermarket adjustable rear sway bar with square design
Rims that just don't have that much clearance facing the inner wheel well- depends on design.

205/45-17 would be safer due to less wideness or 215/40-17 would be safer due to small outer tire diameter. But each has some compromises- less tire selection with 205/45 and rougher street ride with 215/40. 225/45-17 would result in more risk for rubbing due to much larger outer tire diameter.

+42 offset 17x7 with Michelin Pilot Exalto PE2 should be fine for R56 with stock suspension.