Considering the current diversity of coalition air fleets in some parts of the world (the Horn of Africa situation comes to mind), can Russian-built tankers refuel NATO probe-and-drogue receivers, and vice versa? (Say, a US Navy F/A-18E getting a helping hand from an Indian Air Force Il-78MKI, or an Ethiopian Air Force Su-27 filling its tanks from a Royal Australian Air Force A330 MRTT?)
The drogue system was standardized in the 50s and reverse engineered by the USSR in that time so nearly all aircraft that use it are compatible with each other.
Can Russian-built tankers refuel NATO probe-and-drogue receivers, and vice versa?
The Russian system is called UPAZ and its manufacturer Zvezda states
The nozzle assemblies are adapted to the refueling pods of foreign aircraft
Basically this means a bog-standard Russian Mig/Sukhoi cannot plug into a Western tanker aircraft without some change in the configuration.
Say, a US Navy F/A-18E getting a helping hand from an Indian Air Force Il-78MKI
The Indian IL-78s have Israeli-made refuelling equipment so I can't say whether it's compatible with F/A-18E. However, from what I know, India has been using this Israeli equipment to refuel its MiGs and Sukois just fine.