The old masking tape can bake on especially if left in strong light! Old cellophane tape for that matter as well.
When I collected vintage fabrics, some of those had adhesive labels of some sort that also became one with the fabric, in some ways the information on those tags could be invaluable, in other ways always annoying to lose even an inch of vintage fabric.
Sort of related, but we recently had a thread about rusted items in fabric, stapled on price tags often rusted in, especially in a humid climate like Seattle. I make sure that tape is temporary and remove it when I'm done. Likewise, I have brass safety pins and archival paper tags to write notes on. I modern fabrics I sometimes write a note in the selvedge.