That’s just one doctor’s opinion. I would like a second opinion. I am particularly suspicious of his saying black mould is not allergenic. That seems counterintuitive to me. Ventilation, ventilation, ventilation (natural or with well designed technology) is the cornerstone of healthy buildings. Kill with a specialist cleaner, far more effective than just bleach. I guess feather duvets and pillows are equally washable as long as they are refluffed in a tumble dryer afterwards. They do attract clothes moths more than synthetics though. Personally I am more keen on cotton filled duvets for the Summer, cool, heavy and easy to wash.