I just finished a class where we used Steam a Seam 2 (the 1/4" variety) to tack down the binding before we sewed it down. The teacher was very specific about the fact that the Steam a Seam 2 would NOT hold up to multiple washings - similar to a washable fusible it will wear off after about 10-12 washings.
This was on 100% cotton - not muslin and we were making quilts for charity and personal use that were expected to be laundered.
That being said: 1) sew it down and 2) use a lightweight stabilizer.
Show us what you are making!