I double ruler my cross grain cuts and almost never use the cutting grids. I use a 12 1/2" square ruler along the fold and the 24" long ruler to lay across the fabric to cut. If the lines on the two rules line up with the folded edge I know the cut will be right. That is of course after I fold the material straight.
I do use the angle markings for cutting 45 and 60 degrees. But I always do the double ruler with that too.
peace