I tend to think that market-watchers (and the FOMC) underestimate how much that Fed fund futures contracts are pricing in tail risks, rather than a real implied forecasts of where rates will be.
You can see that in the price action today, with 5 bps of cuts now priced in for the June 14 meeting, or a 20% chance of a cut. The market also now sees 99 bps of easing before year end.
One way of looking at that is that there's a 50% chance of a 200 bps cut and a 50% chance of no cut at all. That's because of the chance of a deepening banking crisis. In that case, the Fed will be forced to weigh the possibility of premature easing against the potential for a banking crisis (or to stop a banking crisis).
Because the banking issues and debt ceiling issues are centered in the US at the moment, the dollar is being hit harder than other currencies, despite risk aversion. There is also the possibility that if the Fed is forced into moving due to the banking crisis, then it could stoke another round of strong global nominal growth and inflation.