I'm not a starcher but I am a pre-washer and finish with a nice crisp pressing. I do a ripped edge on one end before I pre-wash. Sometimes due to processing things you still aren't perpendicular on the rip end even if you are on grain. You can tug on fabric diagonally if there is a clear direction/error, but that can also distort the middle. Those selvedges are often more trouble than they are worth and cutting them off can release tension and make fabric behave much better.
But, I also disregard grain line all the time. I fussy cut and generally have no problems with good fabrics. Designs are often deliberately made to "drift" and can be an inch from one side of the fabric to the other if you are cutting along a pattern.
I think a straight edge is the important thing -- so long as you aren't getting any deep Vs in the folds as you cut and all the cuts are straight. I think that being just slightly off grain may actually help shredding or entire threads coming off the edge -- or at least I seem to be covered with more threads than my less grain aligned friends. Whether by my preparation of folding or minor cutting errors, I do have to true up/straighten everything every 3-4 cuts.