It would need serious study by Islamic scholars (in islamic majority countries) to begin with...and then concerted application (say well past the Jews, which I believe is the context here) using it as a credible primary basis.
Only place I have seen something of this nature being done (in islamic majority without going secular/western route) on first principles in good faith basis is Indonesia (but it was not done through medina constitution way or islam-derived way...rather a real-politik way similar to the drive Ataturk did in Turkey)....though I believe in Indonesia case atheism/agnosticism is not legally accepted which I find odd.
Whereas most other Islam-majority countries simply go with the legal body found in Sharia (which names Jews and Christians as fellow monotheists in the same religious lineage aka people of the book...but leaves questions of interpretation for all other beliefs and non-beliefs)....or they have western+secular law alongside it in some way....or in case of Turkey entirely go the western route.
Maybe
@saiyan0321 can give us brief summary of the medina constitution relevance/strength to a nation-state today...and if he feels there are viable routes to found a modern constitution on it's basis...that would say work soundly in the real pluralistic+secular world yet still hold strong religious credibility and affinity for islamic-majority populations.
Like what is the current debate w.r.t medina constitution and sharia given there is much more jurisprudence legacy and precedence of the latter being applied...and thus the likely bulwark it occupies naturally in islamic world for this topic that simply cannot be circumvented to a new appraisal/innovation of say the medina constitution from first principles. If this is the case, then I think its mostly conceptual exercise given this kind of thing would have to be treated seriously (and strived+applied) by large muslim populations to begin with.....before others really take notice for study and analysis.
Right now I don't see that happening (a new innovative alternative), since you have a good working compromise already with common/civil western law....and you can add personal law sharia to muslims on top if the society feels it acceptable (or say the rulers feel thats the best option).....or the other route: simply go sharia law fully.
Both these have weight of rulings and precedence in volumes...its large inertia...hard to develop and sustain something new.
