I would think the copper, no hormones, one would be OK (though it IS introducing something into the body, and the body can always react to things that are put inside of it!!!), but the hormonal ones would cause the same issues that hormones can cause.
I think it's interesting that the Mirena says "non-estrogen", and if you don't read further a person (general, typical, non-reading person, not talking about anyone here) might think that means "oh there are no hormones!" And yet, that's not true. http://www.mirena-us.com/faq.html?C=&c=S1