mmt even strictly as an economic theory separated from macroeconomic policy isn't really descended from marx, my understanding is that there was maybe a little bit of interplay way back when liberal economists weren't sure yet that fiat could work as a money commodity but after that all of these related ideas like role of the state in guaranteeing public welfare with monetary policy and the idea of inflation as a substitution for taxation flowered independently within bourgeois economics, and that's what mmt as formulated today draws on. it's not surprising, economics is the priesthood of capital; financial capital is ascendent but monetarism doesn't work to check the destructive instability of free markets, the inefficiencies of specie and taxation are a constraint on growth, and mmt's explanations in terms of circulation suggest solutions that avoid challenging relations of production. it's not contrived, this is the actual social basis for the development of the theory. you can see premonitions of this in marx's time, proudhon argued against liberal monetary policy from a petty bourgeois perspective (i.e. while maintaining private production) but marx insisted that he and the liberal economists were all missing the real point that production ultimately gives rise to money and not the other way around:

Now suppose that the Bank of France did not rest on a metallic base, and that other countries were willing to accept the French currency or its capital in any form, not only in the specific form of the precious metals. Would the bank not have been equally forced to raise the terms of its discounting precisely at the moment when its ‘public’ clamoured most eagerly for its services? The notes with which it discounts the bills of exchange of this public are at present nothing more than drafts on gold and silver. In our hypothetical case, they would be drafts on the nation’s stock of products and on its directly employable labour force: the former is limited, the latter can be increased only within very positive limits and in certain amounts of time. The printing press, on the other hand, is inexhaustible and works like a stroke of magic. At the same time, while the crop failures in grain and silk enormously diminish the directly exchangeable wealth of the nation, the foreign railway and mining enterprises freeze the same exchangeable wealth in a form which creates no direct equivalent and therefore devours it, for the moment, without replacement! Thus, the directly exchangeable wealth of the nation (i.e. the wealth which can be circulated and is acceptable abroad) absolutely diminished! On the other side, an unlimited increase in bank drafts. Direct consequence: increase in the price of products, raw materials and labour. On the other side, decrease in price of bank drafts. The bank would not have increased the wealth of the nation through a stroke of magic, but would merely have undertaken a very ordinary operation to devalue its own paper. With this devaluation, a sudden paralysis of production! But no, says the Proudhonist. Our new organization of the banks would not be satisfied with the negative accomplishment of abolishing the metal basis and leaving everything else the way it was. It would also create entirely new conditions of production and circulation, and hence its intervention would take place under entirely new preconditions. Did not the introduction of our present banks, in its day, revolutionize the conditions of production? Would large-scale modern industry have become possible without this new financial institution, without the concentration of credit which it created, without the state revenues which it created in antithesis to ground rent, without finance in antithesis to landed property, without the moneyed interest in antithesis to the landed interest; without these things could there have been stock companies etc., and the thousand forms of circulating paper which are as much the preconditions as the product of modern commerce and modern industry?

We have here reached the fundamental question, which is no longer related to the point of departure. The general question would be this: Can the existing relations of production and the relations of distribution which correspond to them be revolutionized by a change in the instrument of circulation, in the organization of circulation? Further question: Can such a transformation of circulation be undertaken without touching the existing relations of production and the social relations which rest on them? If every such transformation of circulation presupposes changes in other conditions of production and social upheavals, there would naturally follow from this the collapse of the doctrine which proposes tricks of circulation as a way of, on the one hand, avoiding the violent character of these social changes, and, on the other, of making these changes appear to be not a presupposition but a gradual result of the transformations in circulation. An error in this fundamental premise would suffice to prove that a similar misunderstanding has occurred in relation to the inner connections between the relations of production, of distribution and of circulation. The above-mentioned historical case cannot of course decide the matter, because modern credit institutions were as much an effect as a cause of the concentration of capital, since they only form a moment of the latter, and since concentration of wealth is accelerated by a scarcity of circulation (as in ancient Rome) as much as by an increase in the facility of circulation. It should further be examined, or rather it would be part of the general question, whether the different civilized forms of money – metallic, paper, credit money, labour money (the last-named as the socialist form) – can accomplish what is demanded of them without suspending the very relation of production which is expressed in the category money, and whether it is not a self-contradictory demand to wish to get around essential determinants of a relation by means of formal modifications? Various forms of money may correspond better to social production in various stages; one form may remedy evils against which another is powerless; but none of them, as long as they remain forms of money, and as long as money remains an essential relation of production, is capable of overcoming the contradictions inherent in the money relation, and can instead only hope to reproduce these contradictions in one or another form. One form of wage labour may correct the abuses of another, but no form of wage labour can correct the abuse of wage labour itself. One lever may overcome the inertia of an immobile object better than another. All of them require inertia to act at all as levers. This general question about the relation of circulation to the other relations of production can naturally be raised only at the end. But, from the outset, it is suspect that Proudhon and his associates never even raise the question in its pure form, but merely engage in occasional declamations about it.

production begets money which feeds back to further production, but production is the primary regulator. you can try to find insights in mmt if you want to flesh out the money->production leg of the dialectical loop - hudson leans (way too) hard into this and graeber flips the precedence entirely upside down - but since mmt as such was developed to exist as a myopic slice of "the question in its pure form" I think it's fair to say that it's non-marxist