I recently bought an R53 that came with 2 good tires about (65% tread left) and 2 bad tires (low tread and loud!). I hate to throw away the 2 good tires and funds are tight right now. I found a good deal on 2 used Eagle GTs with 7/32 tread left for $100, which would probably get me through another year or two and allow me to save up for great tires.

However the 2 existing tires I'd keep are the stock 205/45/17 while the new Eagles I'm considering are 215/45/17. Would this be a problem?

That's a difference of about 4.5mm (or 0.18") in diameter. Will that matter? I'm used to AWD vehicles where your tire diameters must be very close, but I'm not sure with a Mini.

 

No issues. Keep the 205 up front.

 

You'll be fine so long as you pair the wheels front to back rather than side by side.

 

The ABS, traction control (if present), and the flat tire monitor (gen I only) functions may not work
properly with different diameter front and back tires, but in this case, it's probably close enough.
On a gen 1 MINI, if the flat tire monitor will initialize and stay off with them in place, they're probably
close enough for the abs and traction control functions to work as well.
By the way, it's actually about 9 mm/0.354" difference in diameter (4.5mm/.18" difference in radius)
or about 1.5% difference between the two sizes.
To look at it another way, a 215/45/17 worn down to the 4/32 tread would have the same diameter
as a new 205/45/17 with full tread, and most people don't have any problems with a worn front set
and a new rear set of tires of the same size on their car.
A worn pair of 205/45/17 and a new pair of 215/45/17 might be far enough off to matter, though.