Very interesting, indeed!
Eczema and other allergies run in both our families, and my first born was acutely impacted by the vaccination schedule that she was subjected to. Deep, long-lasting health issues developed that correlated with vaccination. In the case of my second baby, we have not vaccinated her at all, and cannot imagine doing so in the future.
So, it seems that in our case, at least, these words of warning would have made a world of difference.
Makes me sad.
The smallpox vaccine actually infects people with vaccinia. Vaccinia is an actual disease and can be passed to other people. It is typically very mild and remains localized tothe injection site, but can cause serious illness occasionally in those with eczema (or a few other skin conditions too) whether the were actually vaccinated with it or whether they catch it from someone else.
Vaccinia is very closely related to cowpox virus, the original virus used in the smallpox vaccine. Cowpox is very, very rare, but it is still around and people do occasionally become infected with it, usually from cats who get it from rodents they catch, rodents being the most common carriers. Cowpox is also generally a very mild illness, but it carries the same risk of serious or even fatal illness in rare cases in people with eczema.
Patients with eczema shouldn't be vaccinated for smallpox not because it is a vacine but because infection with these pox viruses, whether naturally or by vaccination, has a greater risk for those with eczema. Are measles, mumps, rubella, pertussis, etc. much more dangerous than usual when combined with eczema? I couldn't say for sure, but I've never heard anything of the sort. I don't think that saying eczema is a contraindication for smallpox vaccine has any meaning at all in regards to other vaccines unrelated to pox virus.