So far, the copper has had no effect at all on the fabrics ...or the burgers
However, the fabric does get hot fast, and on both sides at once, It takes no time at all to press. I think it would be very easy to scorch if using starch or steam....I don't use either. Just a quick spritz of water from a bottle.
Also..the copper sheet is hot to the touch wherever the iron was placed, so care is necessary to avoid burns. Just like with a hot iron.