I've not had any issues with thread bleeding on my quilting. And, of course, not with piecing either. I hand quilt and use 'hand quilting' thread which is thicker/heavier with no issues. Decades ago when I embroidered, yes, some would bleed onto the fabric but always washed out. I progressed to needlepoint. Very fine canvas and using embroidery thread vs wool and have had no issues with those - even red - bleeding either.