I prefer to have my fabric cut.
Some tears don't do much "damage" - I've seen some where there are pulls on the rest of the fabric as far as one inch -
If there is a piece where I am feeling compulsive about getting a "true" grain, then I will pull a thread - a lot more time consuming, but much less fabric damage that way.
Many fabrics will "revert" to whatever they want to be when washed and dried. I used to do the "tug of war" to attempt to straighten them. When laying around, some of them went back to what they were. So now I usually just deal with how the fabric is after it's been washed and dried.