I am not aware of a "standard" but there are numerous recommendations that are cited and a web search should locate them. However, I have experienced fluid induced instability (subsynchronous activity at 45% to 46% of running speed) on a large steam turbine (3600 RPM) and testing indicated that the water content was around 3%. With no changes to the machine except for a concentrated effort on water removal, the subsynchronous activity disappeared. There probably isn't anything magic about the 3% number because bearing behavior can be significantly affected by bearing load (unknown) and this certainly wasn't a scientific study, more just an observation initiated by the milky appearance of oil in a drain glass. I would expect for instance the threshold to vary significantly depending on whether the bearing was operating in a laminar vs. turbulent regime.
Oil Labs have limits for water in turbine oil. They will alarm given water ppm meets that level. Typically we want to keep the water ppm below 200 in our turbine generators. This is an ISO 32 oil. It has been significantly higher than 200 ppm without wiping bearings but it will cause reduced life of the oil and can create rust of internal components. Of course, the lower ppm the better.
Recommend checking with the oil and machine manufacturer and the labs you do business with for details.
The only official reference I have on hand is ASTM 4378-97 that shows a warning limit of 0.1% or 1000PPM. Way too high IMHO. That standard has been replaced by ASTM 4378-08 which might have some updated info but I don't have a copy so I'm not sure. Personally I wouldn't run at 1000PPM without taking some immediate action to knock that down. I like 200PPM as a target. Is there an ISO code out there somewhere?
ASTM 4378_2008 Standard Practice for In-Service Monitoring of Mineral Turbine Oils for Steam and Gas Turbines. You can purcahse that at ASTM web site.
That std Table -3 provides guidelines for interpretation of Test data and recommendation. According to that water content limit is 0.1 % , ie water content exceeds 0.1% you have to investigate for potential causes and fix. In general in steam turbine water vapor ingression in the lube oil system is possible due to poor intact of seal /loss of barrier seal air or from other sources such as gaskets leak in lube oil cooler. Though investigation would help to solve.
As mitigation you can run centrifuges to separate water to avoid potential issues with oil quality
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