There are a number of ex military jets that are part of the warbird community. However they are only in particular countries that allow them to be on their civil register. For instance US, NZ, Aust and UK.
Most of them are usually ex trainers such as the Jet Provost, Vampire, L-29 for instance. Reason for that is they cheaper to own and operate. Also they are usually less complex to fly. Most of the more serious war birds have very strict requirements before the CA authorities will allow someone to fly it. From memory I think when an ex Swiss Hawker Hunter was doing the NZ warbird circuit a few years ago only the late Air Marshal Sir Kenneth Hayr was given CA clearance to fly it. Other ex RAF Hunter pilots later got clearance but only them.
It is not just FMS requirements that are placing restrictions such as the NZ - US case. A lot has to do with whether or not the actual aircraft are relevant for their intended future task. In the NZ case not having digital cockpits make the NZ aircraft unattractive to third parties as their future utility as trainers of pilots for 4th Gen+ fighters is becoming marginal.