I, too, wash my fabrics. In fact, last year I decided to wash all of my fabrics, that is my collection of fabric from the last 30+ years. Was that a chore and or what? It has taken me over a year doing it, but now I know that when I grab a piece of fabric off the shelf, I don't have to worry about whether it is washed or not.
I clip the corners of the fabric. I use a thimbleful of detergent that is for baby clothes. Some fabrics will not bleed until the soap is in the water. I toss in one of those 'color catcher' sheets, sometimes 2 sheets if I think that there will be a lot of extra dye in the wash (especially for a load of red or dark color fabrics). I put it on gentle wash, warm water and shorten the washing time on the washing machine. Then I take them out of the washer and cut any long threads so the fabric won't tangle in the dryer. When the dryer goes off, I fold them immediately. Since I am a tactile person, I actually enjoy doing this. Please note: I don't use any softener of any kind. You want your fabric totally clean. Softener will just make your sewing difficult with limp fabric.
When I do iron my fabric (because I am using it)I only cut off what I need and iron AND starch the fabric. The stiffer the fabric, the easier it is to be accurate when cutting and sewing.
One of the reasons you DON'T want to iron the fabric is that you don't want to press a crease in the center of the fabric. Sometimes it is very hard to iron out when you do finally need the fabric. Just folding it without ironing will help this problem.
A lot of people have chemical allergies and aren't even aware of it. Handling unwashed fabrics and touching your eyes, nose and skin can cause quite a reaction. Often times it is a reaction that builds up over time and then BOOM you suddenly have an itchy rash and you wonder where it came from.