Twenty years of quilting here and I can tell you the tackiness question almost never comes from the scraps themselves. It comes from execution. A scrap quilt that looks chaotic or has wonky seams reads as thrown togather. One with a clear plan behind it reads as thoughtful, full stop. What makes the difference, in my experience. Pick a structure first, like a consistent block size or a color progression across the rows, then pull scraps that fit it. Trim every piece to uniform dimensions before sewing, even if it means the finished top is smaller than you planned. Press your seams the same direction throughout. And use one fabric family for the binding so the whole thing looks intentional rather than salvaged.
The other thing people worry about is the recipient noticing it's scraps. Most non-quilters genuinely can't tell, or if they can, they assume it took more skill, not less. Working around odd shapes and limited yardage is harder than buying three yards and slicing it up. Last tip that never fails me. Add a small handwritten label on the back with the date and a line about where the fabrics came from. It turns 'made from leftovers' into 'made from memories' and nobody has ever called that tacky.