Fabrics shrink differently when washed alone compared to being washed as part of a quilt. Quilting binds the fabric to the batting. When there is enough quilting, the batting controls the fabric shrinkage. In other words, the fabrics cannot shrink more than the batting shrinks.
How much is enough quilting? Not sure. Certainly doing SID quilting around 12" blocks is not enough quilting to prevent uneven fabric shrinkage in a quilt. In my experience, a large meander is sufficient quilting. I do not consider this to be heavy quilting; just moderate quilting.
I was fortunate enough to be able to take a class from Harriet Hargrave years ago. HH advocates not pre-washing fabric, although she does advocate pre-testing every fabric for color fastness before using it in a quilt. She brought a flannel quilt she had made as proof of the shrinkage thing, because flannels shrink more than other fabrics and also shrink in different amounts among themselves. She made a quilt out of unwashed flannel, quilted it, measured it, washed it, and measured it again. It shrank about 3%, the amount that the batting was supposed to shrink. It did not shrink the horrific 10% or 20% one might expect from unwashed flannel. And the quilt was beautiful.
The same thing applies to grain. You could make a quilt out of squares that all had bias edges IF you could keep those bias edges from stretching and distorting while working with them. I find that heavily starching fabric before cutting is enough to keep even bias-cut strips from distorting while I am sewing. Once they are in the quilt and become part of the "quilt sandwich" by means of the quilting, anything off-grain is not going to be affected by washing. Again, there has to be "enough" quilting for this to work, and I would estimate "enough" at a large meander.
I do not pre-wash fabrics. I do not bother to straighten grain on fabrics before cutting. However, I do test for color fastness of suspicious fabrics before using them in a quilt, and I am careful to cut fabric at a strict 90-degree angle to a fold. This approach may not be for everyone, but it saves me tons of time and makes quilting a lot more fun for me!