I most always have my borders on the lengthwise grain. When your fabrics are on the crosswise grain you can get some stretching. Fabric will "stretch" more on the cross grain than length grain.
I take the finished width of the border and add 1 inch. I will clip the fabric and rip to the other end. Then I will fold up the border fabric to trim off the ripped edge. Usually this edge will curl just a bit. Then I apply my borders to the quilt. At this point I have not taken off the whole inch that I added for the ripping. This little bit of extra fabric gives me enough room to square up my quilt top and have my borders lay flat.
The stretch of the cross grain border really shows up when you load the quilt on your longarm frame in prep for quilting.
Also, ripping on the lengthwise grain you will get a straight line.
Hope this helps.