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if you're covering the outside with insulating panels, the notion of walls breathing is somewhat moot
No because the panels can (and IMO should, for as building with solid walls) be breathable.
I'm pretty sure we're going to use wood fibre panels, which tick all the boxes of being breathable, hygroscopic and have good capillarity, but also sequester carbon.
If you then do render them you need a breathable render, like lime, but as we're cladding our place with viroc cement boards, my current understanding is that we shouldn't need to render.
Re: rendering - if you're covering the outside with insulating panels, the notion of walls breathing is somewhat moot.
Saying that, I'd probably remove it, because I hate it.
Re: rendering the insulation - yes, but just not with lime. That would be a bit pointless, no? You've just chucked up a bunch of pretty impermeable panels, and you choose a fiddly, expensive, hard to find the trades, medium to cover it, whose sole advantage is that it is breathable, and should go on solid walls.