I've never had a problem with self-adhesive stabilizers gumming up my machine, and I look
and clean often. Seems to me one would see it building up on the needle, before it got down
into the machine....since it is the needle that would carry it down into there.
I have tried using self-adhesive hook and look tape, and THAT was a disaster. Talk about
gumming up everything! Besides that, it really doesn't hold very well.
If you're concerned about the glue, you could use the kind that adheres like the sticker part
on an envelope. You apply a little water, and that makes it stick (no "gum" there).
Depending on what you're stabilizing, you may not need an adhesive at all. When I'm stabilizing
a straight seam in a garment, and I want to make sure it doesn't pucker, I use plain old
newsprint paper, cut in strips. Works great, and tears away so clean there are no bits left
behind. It only comes in a manila color, that I've found....and of course if you have any
zig-zag stitching it would stay under that (can't remove).
You can also tack down non-adhesive stabilizer with a bit of fabric glue...or elmers glue, Or,
don't tack it down at all. That works too.