At least since King and Plosser 1984, the core prediction is that prices are procyclical and perhaps a leading indicator as well. Think of inside money/credit as another input into production, and real business cycle theory as showing a general comovement of economic variables. That means broader measures of the money supply go up in good times and fall in bad times. Of course you don’t need real business cycle theory to get to those rather general conclusions, but they are fully consistent with real business cycle theory and will fall out of most sensible models with credit.
Now consider prices. If money supply expansions/contractions come more quickly than output expansions/contractions, the price level will be pro-cyclical in an RBC model, at least during the early stages of the cycle before other outputs adjust. Especially on the upswing it is easy to imagine how optimistic expectations give rise to some M2 which comes before the actual output rise. And in bad times the broader aggregates won’t put much pressure on prices. You can think of the broader “comovement effects” as outweighing possible interest rate effects.
Paul Krugman has a post attacking a bunch of people, but he is not focusing on what RBC models actually imply, and have implied for a long time. (He sticks with attacking the easier target, namely those who predicted very high inflation from the high monetary base.) It is not that “RBC models explain the crisis,” but rather demand and supply side models have more in common than is often recognized, all the more once you move beyond the immediate short run.
Furthermore there is nothing in the behavior of prices which rules out a significant (and I would say non-exclusive) role for the supply side. On top of that the pure demand side theories predicted more deflation than we have ended up seeing and thus they would do well to incorporate some supply-side considerations.