I suspect that's accurate, but I'm not sure. The RDY-2s in the Mirages are 1990s tech so likely have limited IFF abilities, and they don't carry any extra IFF gear. I can't find anything specific on the RDY-2's ID range (just a quick search), but it may be classified.
That's why fighters are best used in conjunction with AEW aircraft or other large radars that are better at long range identification. In a war context, it may be the case that all civilian traffic is warned off, so anything that's not yours is treated as hostile.
I tried different aircraft though I didn't use the most modern ones because I had the impression that IFF devices in every aircraft help to the classification of unknown contacts.
Surely not indentifying the type of aircraft, but at least if it's enemy or friend.
I don't think IFF is modelled in CMP per se, but even so, I think the simulation is correct in its "Normal" awareness mode. From the Wikipedia article (https://en.wikipedia.org/wiki/Identification_friend_or_foe):
Despite the name, IFF can only positively identify friendly targets, not hostile ones. If an IFF interrogation receives no reply or an invalid reply, the object cannot be identified as friendly, but is not positively identified as foe; it may, for instance, be a friendly aircraft with an inoperative or malfunctioning transponder.
Also, it is an option in the scenario editor to set a side to have an "auto side ID" awareness level. Auto side ID mode behaves similar to how you are describing, and you could very well have played scenarios in that mode in the past. But that will be a scenario-to-scenario difference and not CMO version-to-version. It's really up to the scenario designer.