From Esther comes this word of warning. She describes a situation in which her niece had a bad reaction to those tagless labels. I don’t know if she updated the entry but in a private email, she said:
My sister sent me an update on the problem. It appears that the re-formulated paints may include latex tainted paint, similar to silk screen paint. My niece had another reaction even worse than previous because her entire back flared up red. The pediatrician suggested my niece now has a latex allergy and possible nickel allergy. Latex allergies can develop over time with multiple exposures.
There’s a photo of her niece’s back on site. It’s not a mere reddening of the skin or a rash but looks quite painful. Just something to consider if you use those iron on tags.