Frixion pens specifically say Do Not Use on fabric. Reappearing lines may not be so much of an issue in warmer climes. However, if you have ever seen antique signature quilts where the ink has rotted the fabric, is this what we may experience in the future using Frixion pens? I am not a chemist, so I can't speak on the ink ingredients, but I would like to believe the people who signed the antique blocks thought their ink was safe. I am not going to chance it.
Just my thoughts...