I don't stretch it at all unless I am working on squaring the fabric up before applying the borders (then I wet the fabric & gently pull it back on grain/to the proper shape). I do press my quilt top before measuring. This last quilt I had was off 1/8" one direction & 1/4" the other direction. I just took took the median number (middle number when arranged from smallest to largest) and went with that. Borders turned out perfectly.
What I did to make sure they worked out was to put a pin in the middle of the side of the quilt top & the middle of the border. I pinned there, then pinned each corner & then kept pinning in the middle of each set of 2 pins until the fabric was basically flat. Then, I sewed & lo & behold I still ended up with a square quilt. Next time I will do a better job cutting, but you can make it work as long as it's not a huge difference (I'm sure it's not -- you would have noticed that before now).