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Yeah I'm not good with the longer words. Woodfibre insulation and clay plaster are often mentioned as useful moisture buffering materials - they can absorb some moisture then give it up again, which reduces condensation on surface (in the case of clay plaster) and regulates humidity. I think the problem with gypsum is that it doesn't like to give up the moisture again, and it's a good nutritional base for mould. And people usually cover it in plastic paint.
I know nothing about gypsum's hygroscopic properties, but hygroscopic materials can absorb moisture from the air then release it again. Ideally in an older building this will be over a longer period of time, as this is less likely to cause problems.
I'm currently deep down the rabbit hole of how to insulate an early Edwardian terrace to modern standards without causing damp problems, so in my case I need breathable insulation but ideally it will also be hygroscopic.
For example, if I use mineral wool it is highly vapour open, but has poor hygroscopic and capillarity characteristics. In practice, this means that if it does get wet, it takes a long time to dry out. Plus wet mineral wool will usually sag with the weight of the water (because it's non-hygoscopic, so doesn't absorb it), which will create gaps around the edge where the heat will escape causing condensation on the walls.
This is a problem caused not by lack of breathability, but non-hygoscopic materials, i.e. a moisture issue, but not the one you'd think, so I think this is what you mean @hoefla ?