First, I want to admit that I am not a pre-washer of my fabric. I tried it and the mess and dealing with all that fabric and the strings was just horrible. I lost several inches. So, pre-washing is such a personal preference. Yes, I have had fabric run after the fact and I just fight it with color catchers.
If you tear your fabric, regardless of whether you wash it or not, you will lose a lot more than you will gain by having it on the straight of grain. Think about it....Our pieces are so small that it just does not matter.
I do iron the center fold. Often the original fold has extra bumps or lumps and that will never make a straight strip. If I am cutting a long border, I will cut it so that the print is straight for my border. So, if I am cutting a little bit on the bias, I just don't care. I have gotten smarter, and try not to make a border out of a fabric that has to be lined up accurately for the borders to look good.
Edited to add: Now, if you decide to use your cotton fabric to make a gathered skirt or even a blouse, getting the fabric straight can make or break your project. These type of projects do not have a backing or padding in them and stitched together to make them stay straight. They hang like you cut them. Cutting the front part of a blouse on the bias could give you some interesting saggy parts. The same goes for a skirt. So the advice about straightening by tearing or pulling a thread should be followed.
Last edited by Barb in Louisiana; 02-17-2020 at 08:21 AM.