This just does happen with Fat Quarters. It is the nature of the beast. You have to plan accordingly if you don't want to loose out on necessary yardage.
I have had decent success with minimum raveling by doing small loads on a very gently cycle. I wash with baking soda and put White vinegar in the water softener part. Tumble dry gently. I think the key is to not put too many In one load.
I love fat quarters! I predominantly quilt with fat quarters. I LOVE variety. I'll deal with the raveling.
The other thing you can try is stitch around all 4 sides close to the edge with a basting stitch and see if this helps. Before washing. Me, I'm not interested in taking the time or wasting the thread. But, thought I would throw it out there as an option.
These suggestions are just my opinion. I'm sure you'll get many helpful suggestions to choose from.