I have often seen recommendations to use only unbuffered acid-free tissue with protein-based materials (such as silk and wool textile, organic archaeological items) and archaeological metals but I haven’t come across a recommendation regarding black dyed textiles.
There is an interesting article on the possible effects of buffering agents on dyes in http://56×56.com/for-photographers/buffered-vs-non-bufferedunbuffered-materials-for-digital-pigment-prints/
and another article on dyeing fabric black with sulfur-based dyes which gives food for thought: http://www.denimsandjeans.com/denim/manufacturing-process/acidic-damage-in-the-sulfur-black-dyeing-of-denim/
There are at least three potential reasons to be concerned about using buffered acid-free tissue:
1) the acid-free tissue only has a neutral pH because of the presence of calcium carbonate or similar buffering compounds – as the tissue ages its integral acidity will increase
2) the buffering agent could react with the dyes or their deterioration products in ways which are unknown or not widely known. If in doubt, don’t add potential complications to the system. There has not been much published in the conservation world on the long-term stability or deterioration of modern dyes.
3) there is a possible physical effect of the buffering material showing up as a pale powder on the dark fabric. I haven’t come across this happening or heard of it being noted, but it could be behind the suggestion that unbuffered tissue is preferred for use with black fabrics.
The safest option, I think, is to use unbuffered acid-free tissue next to all textiles, especially when they are dyed with unknown dyes and printed with unknown screen-printing inks. More expensive, but hard to criticise !
Hope it helps