There's no such thing as late-stage capitalism. The entire idea is based in the neo-Marxist material dialectic, a claim that history proceeds in set patterns. When someone tells you they can predict history? You should laugh at them. At best, you can compare the present to similar past civilizations. Those comparisons work best when the comparisons are more specific in nature- for example, comparing the topsoil loss via farming between today and ancient Sumeria, or income inequality rates compared between us and the Roman Empire.
Admittedly, things are pretty shitty right now. High income inequality, ballooning lower class debt, etc, etc- it sucks. But if there is one thing that history should teach us, it's that things getting worse sure as hell isn't an indicator they're about to get better. The entire idea of late-stage capitalism contains an element of "it's causing our problems, when it collapses the problems will go away as well."
This isn't to say that sins of historical thought are limited to advocates of the idea of late-stage capitalism- its foes often fall into equally severe traps. The "end of history" is often used as a counterargument against late-stage capitalism. Its sin is assuming change will not occur, which is frankly worse than assuming you can predict the direction of its change.
This isn't necessarily a critique of neoliberalism or neo-Marxism, just of the way they address history. Whenever you assume that you can understand history through the lenses of a single theory, that theory will fail you. History is the sum total of all human activity and the natural forces acting upon it. We need to respond it its twists and turns, rather than expecting it to conform to our expectations of it.