How Japanese neutrality would change Royal Navy deployments

If Japan did not enter World War II, would the Italian Navy face more Royal Navy forces?

Yes. Britain would retain more strength in the Mediterranean and would not need to build the same emergency Eastern Fleet from other theatres.

Italy would remain the largest active Axis naval threat, so British strength would stay concentrated in the Mediterranean. Some ships might still deploy eastward as deterrence if war with Japan remained possible, but the vast emergency Eastern Fleet and early Indian Ocean operations such as the seizure of Madagascar would be less likely.