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I believe you can pretty much whack whatever form of conventional insulation in there and not worry about your house getting fucked up...
As I understand it, if you insulate inside a cavity and it changes the behaviour of moisture in the wall, e.g. changing where in the wall is the dewpoint, then it can very much fuck up your cavity wall and thus your house by inducing or accelerating corrosion of cavity wall ties because of the extra moisture.
No, I'm no expert on cavity walls but I think they were mainly introduced to reduce damp problems. But the other advantages of having the air gap between two walls are inherently better thermal properties (even without insulation), better soundproofing and a handy pre-made space to fill with insulation.