We used to get it a lot with split load boards where the N to E fault was on one circuit Ie the lighting circuit, but the Rcd did not trip till the high power glasswasher or the cooler fan on different circuits was used, first choice was get in the appliance people, only to find all ok.As I've been saying to JohnD, that is something which, under normal circumstances, really should not happen - so it warrants investigation. After all, the whole point of having circuits split onto two RCDs is that a fault causing one RCD to trip should not have an effect on the other.
If I were you, I wouldn't 'write off' the microwave just yet, even though it's very likely that it is faulty (even if something else is 'wrong' as well).
Kind Regards, John
Edit: crucial missing word put in!
However with Rcbos, like you say its proberly less rare if at all possible.