I think the "old" woven cottons could be "squared" by tugging and pressing.
Some of the newer ones seem to have a permanent memory for how they were processed - so even if "squared" at one time, they revert to being "off" when left to their own devices.
What I'm comfortable with now:
I buy 100% cotton fabric - I've gotten great fabric at WalMart, and great fabric at LHSs. I've also gotten some PERMANENTLY off-grain Kaufman
fabric at a LQS. (Where the clerk told me that it would straighten out after being washed. NOT)
I overcast the ends before washing to minimize raveling. I use either a narrow, long sigzag stitch on my regular machine or a long stitch, narrow width overcast with my serger.
I soak in hot water, wash gently in warm or cold water, and dry on permanent press.
If it's fairly smooth when I take it out of the dryer, I just fold it and add it to the stash. (Nice fabric). If it's horribly wrinkled when it comes out of the dryer, I'll probably not use it.
I'll iron/press it before cutting it. MANY times the ends are uneven when I fold the fabric from selvage to selvage (and have the fabric lay smoothly) because the threads have gone to whatever their "normal" position is.
I now look at grain lines carefully before purchasing. Sometimes they will straighten out. But if the fabric design is off-grain, there is no changing that.
I will only tear for backings. Sometimes there will be up to an inch of puckering on the torn edges.