You should have zero in/out play...as in you should not be able to push the wheels deeper into the housings or pull them out at all.
Some side to side play is normal (required actually, by design). I've never been able to find a spec by IHI or VW for an acceptable amount. Some MFGs release those specs and others don't.
So, to get non scientific, you should be able to move the shaft side to side, but just a hair. Different specs for different turbos, but some Mitsu turbos are considered within spec until the wheels touch the housings. When you have oil pressure, the oil takes up space within the journal bearings and will take play out of the assembly, so if the wheel can touch the housing when dry, it can still run perfectly fine when wet (oil pressure) but that's the outer limit on those turbos.
No idea the limit for IHI, but being able to move it a hair side/side is normal and healthy. If it's feels sloppy, it probably is worn and on borrowed time. In/out should be zero. Any in/out play is abnormal and cause for concern (either the thrust bearing or the shaft is worn/damaged).
