I always rip fabric for my borders and backs, unless I'm doing pieced border. If I'm using a wide backing fabric then I will wash it first and then rip it since wide backings sometimes shrink a fair amount. I've found that when I rip for long borders or backs I don't have any problems with wavy borders. You don't lose much to raveling unless you're trying to rip some very loosely woven fabrics like homespuns.
It's a fast way to get a perfectly straight, long "cut" from yardage. If the piece is a cotton quilting fabric or cotton backing fabric then I have no problems ripping along both the cross grain and the straight of grain (parallel to the selvages). The secret is to use your scissors to make a 1 to 2 inch cut from the edge of the fabric and then rip fast. I've been doing this for years and have had no problems with it damaging the fabric.
Don't try to slowly tear, that is more likely to cause bunching of threads along the edge which is a pain to straighten out, though it can be fixed, just takes more time.
Also, I don't generally tear home dec fabrics, fabrics with lots of texture or specialty weaves as they will often not tear easily.
Rob