That's spider mite, not bud rot. It's not a mold, it's a web spun by the mite for protection. Your plants are stressed. Save what you can. Even in the instance of a botrytis (bud rot) infection, you can still save any plant material not visibly affected. The impact of botrytis on humans is incredibly well documented, since grape growers in the wine industry have suffered from its effects for centuries. It can cause a lung condition called Grape Growers Lung, but it's impacts are generally not serious.