The purpose of SID is to prevent any distortion. SID is a type of foundation quilting that should prevent your quilt from shifting while you FMQ. If your fabric is shifting & getting distorted from the SID, see if you can adjust the tension on your presser foot to lessen it. Also, with high loft batting (not sure if that's what you're using), certain feet can drag on the fabric. I have to use an open toe with my walking foot (I don't have even feed) because the other 2 options drag too much (one is a regular-type foot, the other is a ditch guide foot).
If you are referring to the thread overlapping your design, I use water soluble thread for my SID work so that I get the advantage of the foundation without creating a permanent interruption in my chose FMQ design.