Why is my ESD wriststrap failing with nitrile gloves on?
Nitrile is not a particularly conductive substance.  In fact it is probably a decent insulator for non-critical purposes.  You shouldn't count on health care or maintenance type gloves being an insulator for purposes of electrical safety (especially as they are so easily pierced), but they are presumably insulating enough at low voltages to fail an ESD test.

You likely need to consider the entire design of your process and procedures, not just what some bench meter says (regardless if it appears to approve or disprove).  Perhaps parts never leave protective packaging or fixtures.  There are also purportedly ESD gloves sold which may be more suitable for your process (or required procedures) than those made for the health care market.