Memes

At their heart, both capitalism and marxism are ideologies describing how things “ought to be.” Proponents of either of them seek to influence political decision making around economic decisions, but neither is/was/will be reality.

No, Marxism does not just describe things as they ought to be. It's main aspects are:

Anthropological: a methodology for understanding how capitalism happens and how it changes to suit changing conditions (many of which it brings about)

Scientific: a process based ideology for developing an understanding of our local conditions and our ability to change them through sociological investigation, mediated through democratic process

The political program extends from an understanding of those two aspects, and is very variable, because the programs are applied to the local conditions of their environments.

You describe science as "a process based ideology" with an aim. Science is seldom described as an ideology. What is your source here? Or, if this is an original idea, can you expand upon what your concept of science as such, is?

There are issues with the other "aspects" of Marxism you briefed above; most salient one being the attempt to infer principles of economics from anthropology (which isn't a particularly robust academic field by itself, devoid of any power to make good predictions in its own field, let alone in others), but I'd avoid opening that at the moment as considerations of "what science is" run deeper.

Capitalism postulates that all capital ought to be privately owned and working in individual interest,

No, that strain of bourgeois thought died out as a ruling ideology hundreds of years ago, when state intervention in some failed ventures if the west indies trading company demonstrated that it is more profitable for capitalism to maintain a strong state to protect profits.

Source, please; and unambiguously capitalist one?

Communists dismiss this by pointing out that inequal access to capital causes internal problems in society,

I mean yeah but that's not the main thing. The main thing that Marxists believe is that as capitalism moves into its monopoly stage, it ceases to be a historically progressive force (in opposition to feudalism) and it starts to be fettered by its own issues, just like feudalism was.

Marxists believe that as production becomes socialized and planned, capitalist control makes these socialized production processes inefficient and ultimately leads to a cycle of crises.

Criticism of monopoly is not a criticism of capitalism. In fact, capitalist theory itself doesn't view monopoly as a good condition. Capitalism prescribes competition and open market - for both buyer and seller sides.

What safegaurds does Marxism/Communism has to prevent monopoly?