2 psu conected as split + and -
Laboratory power supplies' OUTPUTS are floating respect to earth ground. They can do this because they are isolated (have a transformer inside). Anyway, their CASES are always connected to earth ground so you don't get electrocuted when you touch/operate them.

If your supplies are isolated, then it is ok to disconnect their outputs from earth ground... but please keep the earth pin in the plug so the cases/chasis of the supplies are kept at a safe voltage. To do this you have to check first that they are isolated (which is usually the case for PC supplies and voltage adapters).