Would it be safe to connect two identical AC/DC converters in series if they share the same AC source? My concern is that the negative DC output is grounded somewhere in the converters causing the second AC/DC converter to be shorted.
The AC/DC converter outputs need to be galvanically isolated from the AC input. Modern high frequency switchers often use switching transformers to provide the isolation. You show two grounds with ? marks. Select only one to be grounded. You can have a +/-12V or single ended 24V. And keep the DC ground isolated from the AC ground.
Yes, you can gang power supplies this way, as long as they have floating (isolated from mains) secondaries. Choose the lower one’s (-) as a secondary reference. It need not be tied to safety ground but there’s no harm if it is.
There’s no specific requirement to have grounded AC input either. But make sure the PSUs are designed to support that.