You say:

what you mean by ‘material’ also encompasses non-material things, which doesn’t align with how the word ‘material’ is used in philosophy.

All philosophy is class philosophy. Bourgeois philosophy tends not to acknowledge that fact and its obscurity furthers its class position.

Marxists always treat materialism as dialectical materialism. While materialism relates to matter and treats the material as primary, it is matter as a relation as opposed to matter as 'things'. Engels in Anti-Dühring:

Motion is the mode of existence of matter. … On the earth, for example, a body may be in mechanical equilibrium, may be mechanically at rest; but this in no way prevents it from participating in the motion of the earth and in that of the whole solar system, just as little as it prevents its most minute physical particles from carrying out the vibrations determined by its temperature, or its atoms from passing through a chemical process. Matter without motion is just as inconceivable as motion without matter.

Matter, then, cannot be reduced to the physical object that appears to rest in front of you. The object is the relation of all its constituent atoms and forces, always moving. You say that I must mean that '"material" also encompasses non-material things’. This suggests that something like motion would count as a ‘non-material thing …’. While motion is not tangible, it is ‘matter’ according to dialectical materialism.

Marxists do not see motion as falling within the category of matter. Marxists treat matter and motion as a dialectic. If motion is matter and motion is intangible, then other intangibles could be material. That is, not every intangible is reducible to an idea.

Marx, Capital, Volume I (Preface to the first German edition):

… it is the ultimate aim of this work [Capital], to lay bare the economic law of motion of modern society[.] … My standpoint, from which the evolution of the economic formation of society is viewed as a process of natural history, can less than any other make the individual responsible for relations whose creature he socially remains ….

Which is to say that social laws of motion are not inescapable just because society somehow all agrees to be bound in some way (which is an idealist refrain to the power of money that I have heard before), but because these laws (relations) are material. These relations are no less material for being expressed in symbols, linguistic or mathematical. I’m unsure whether you or your sources would consider such relations as material or ‘non-material’ for not being physical – possibly not. Marxists treat these relations of production as material.

I reject the equation of material to ‘physical’ or relating to ‘(physical) matter’ because that definition is neither materialist nor dialectical. The framing suggests a definition of matter from an idealist perspective. This is unsurprising if you consider yourself to be an ontological idealist. It may explain why you thought (in another comment) that ‘“dialectical materialism” … can just as well … work … fine within an idealist framework/alongside subscription to idealist schools of thought’. That view fails to accommodate the motion-matter dialectic and must exclude value, social relations, and laws of motion.

If that’s wrong and you are reading philosophy that accepts the above concepts as material, then we must start again because I have misread you.

Materialism is not a dogmatic system. It is … a way of interpreting, conceiving of, explaining every question.

… Materialism is opposed to idealism. On every question, there are materialist and idealist ways of interpreting it, … of trying to understand it.

Thus materialism and idealism … consequently … express opposite approaches in practice and lead to very different conclusions in terms of practical activity.

This leaves no room to say that ‘Marxism doesn’t conflict with idealism’:

Idealism is the way of interpreting things which regards the spiritual as prior to the material, whereas materialism regards the material as prior. … [T]his difference manifests itself … in general philosophical conceptions of the world as a whole, and in conceptions of particular things and events.

If your philosophy rejects social relations, etc, as matter, it is bourgeois philosophy. Idealist, bourgeois philosophy does not provide the tools to fully grasp the claims of materialist dialectics.

Example:

Why are there rich and poor? [An] … idealist [explanation] … is because some … are careful and farsighted, and these husband their resources and grow rich, while others are thriftless and stupid, and these remain poor. …

The materialist … seeks the reason in the material, economic conditions of social life[,] … divided into rich and poor … because the production of the material means of life is so ordered that some have possession of the land and other means of production while the rest have to work for them. However hard they may work and … scrape and save, the non-possessors will re­main poor, while the possessors grow rich on the fruits of their labour.

Summary (emphasis added):

The basic teachings of materialism stand in opposition to these three assertions of idealism [omitted].

1. Materialism teaches that the world is by its very nature material, that everything which exists comes into being on the basis of material causes, arises and develops in accordance with the laws of motion of matter.

2. Materialism teaches that matter is objective reality existing outside and independent of the mind; and that far from the mental existing in separation from the material, everything mental or spiritual is a product of material processes.

3. Materialism teaches that the world and its laws are knowable, and that while much in the material world may not be known there is no unknowable sphere of reality which lies outside the material world.

… Marxist philosophy is characterised by its absolutely consistent materialism all along the line, by its making no concessions whatever at any point to idealism.

On the broad attempt to philosophise away the differences between materialism and idealism:

[I]dealism serves as a weapon of reaction; and … when socialists embrace idealism they are being influenced by the ideology of the capitalists. … Whatever fine systems of philosophy have been invented, idealism has been used as a means of justifying the rule of an exploiting class and deceiving the exploited.

This is not to say that [materialist] truths have not been expressed in an idealist guise[;] … they have. For idealism has very deep roots in our ways of thinking, and so men often clothe their thoughts and aspirations in idealist dress.

The problem of understanding and explaining development in a materialist way … is answered by dialectical materialism.

Dialectical materialism considers the universe, not as static, not as unchanging, but as in continual process of development. It … seeks for the explanation, the driving force, of this universal movement, not in inventions of idealist fantasy, but within material processes themselves—in the inner contradictions, the opposite conflicting tendencies, which are in operation in every process of nature and society.

Cornforth, quoting Lenin:

“… dialectics is the study of the contradiction within the very essence of things. …”

Where contradiction is at work, there is the force of development.

This materialist understanding of dialectics is the key to understanding the forces of development within the material world itself, without recourse to outside causes.