Στο διαδίκτυο διαπιστώνω ότι δεν υπάρχει κάποια καθιερωμένη απόδοση. Δεν είμαι έτοιμος να προτείνω «ασυμβατότητα». Νομίζω ότι η «διαφιλονικούμενη διαφορά» είναι αρκετά σαφής.

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Note added at 14 hrs (2022-03-22 20:18:23 GMT)
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Όπως λέει η πηγή της Αναστασίας ( https://www.pcr.uu.se/research/ucdp/definitions/#incompatibi... ), το incompatibility είναι «The stated (in writing or verbally) generally incompatible positions». Δηλαδή, «ασυμβίβαστες θέσεις».
Δεν είμαι διατεθειμένος να προτείνω «ασυμβατότητα», όπως είπα, αλλά μπορώ να προτείνω «ασυμφωνία» (Όπως λέμε και «ασυμφωνία χαρακτήρων».)
Πώς λέει το καλό ελληνο-αγγλικό λεξικό στο λήμμα «ασυμφωνία»;
state of disagreement or conflict, discord, disharmony, incompatibility, incongruity (near-syn ασυμβίβαστο 2b):
https://www.greek-language.gr/greekLang/modern_greek/tools/l...

Διαβάζω στο Routledge Handbook of Civil Wars:

UCDP adds an element, originally not found in COW, namely the disagreement (“incompatibility”) between the warring parties. It means it has an elaborate procedure for defining incompatibility and also for dividing conflicts into two types of disagreements, notably those that concern control over government and those that deal with control over territory.
p. 16

Scholarship has only recently pushed the intersection of armed conflict back in the chain to the point where protest activity can move toward violence or cooperative resolution of the incompatibilities [δηλ. των ασυμφωνιών] between the opposition and the state (Salehyan et al., 2013).
p. 321

The third aspect relates to the issues. Conflict resolution concerns the resolution of conflict issues, that is, it is related to the issue dimension of conflict. Conflict resolution requires that the parties come to an agreement that settles or dissolves their basic dispute. In conflict theory, the stated aspirations concerning a contested resource are called incompatibility. Conflict resolution is related to the incompatibility of a conflict.
p. 364

Συμφωνώ με τον Σάββα ότι ως επίθετο το «διαφιλονικούμενο» κολλά (κακώς) στη «διαφορά».
Αναδιατυπώνω λοιπόν:
διαφορά / ασυμφωνία ως προς το διαφιλονικούμενο
ασυμφωνία για το επίδικο


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Note added at 2 days 10 hrs (2022-03-24 16:36:54 GMT)
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Το συναφές κομμάτι στην απάντηση του καθηγητή:

Here is how I see the definition:

There are incompatibilities of many sorts in society over many different things, notably political power, territorial control, but also health services and taxes. Those that are included in the UCDP definition concerns government and/or territory.

Among those incompatibilities some are contested between at least two parties, i.e. include an explicit demand by one side where this demand is resisted by another side.

In the data that is collected for UCDP only those contested incompatibilities are included which involve the use of force by the parties.

Thus there can be many disagreements in society, only some of them give rise to movements that bring them up in the form of campaigns or protests, and still fewer are militarised where the parties use armed force.

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Note added at 2 days 11 hrs (2022-03-24 17:57:03 GMT)
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Σαν προσωρινή λύση, μια και δεν μπορώ να βρω ικανοποιητική λύση για το «contested»: διαφορά μεταξύ δύο τουλάχιστον αντιμαχόμενων ομάδων

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Note added at 4 days (2022-03-26 07:33:59 GMT) Post-grading
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Σχετική συζήτηση στη Λεξιλογία, απ' όπου προκύπτει μια προτίμηση με το ακόμα πιο αντιστρέψιμο «επίμαχη ασυμβατότητα».
https://www.lexilogia.gr/threads/contested-incompatibility.1...