When quilting in the hoop, I only put either the backing or top fabric in the hoop, and place the batting and the 'second' fabric on top or under. I do use a few pins to hold in place but no stabilizer.
My Brothers have never given me problems with thread, I use all sorts.
If using an embroidery design, I would do that first, with batting in the hoop, then put the backing underneath before the quilting is done,
Me Too...When emb'ing blocks or whole quilts no stabilizer. Make your quilt sandwich and go...