> Why are you saying that "capitalism with modern mixed economies" doesn't qualify as capitalism?
I'm saying the 19th century system for which the name “capitalism” was coined was replaced basically everywhere with modern mixed economies which are a different but related system; the two share some features just as 19th Century capitalism and feudalism share some features, but they aren't the same system.
> To my knowledge, it's capitalism through and through
It's not; as many people, not least advocates of reversion to (or at least toward) the 19th Century system for which “capitalism” was coined, have noted, modern mixed economies compromise in fairly significant ways the property relations which both defenders of capitalism and it's opponents (including the ones that coined the term “capitalism” for that which they opposed) define as central to capitalism.
> I also think there's some issue with using "Marxism" to refer to some kind of programme rather than the critique of political economy from the writings of Marx and Engels.
That may be valid on some level, but even if so it's purely semantic pedantry that has no bearing on the substance of the discussion; Marx and Engels laid out a program as well as a critique of capitalism, and when we are talking about concrete economic systems that can be tried out, the program is relevant, the critique is not (it is merely the oriel motivating rationale for the concrete program.) A critique can be believed, but not instantiated.
So, if you want to mentally replace “Marxism” with “the concrete program Marx and Engels proposed to address the Marxist critique of capitalism” throughout the discussion, feel free. But don't expect the usage to catch on when the distinction between the Marxist critique and the Marxist program is generally clear from context such that no additional clarity of meaning would be succeed from making the restriction you propose to the use of “Marxism” even if I've were to agree that their is on done level a basis for that restriction.
> This kind of usage lets you get away with saying that a "mixed economy" is something even close to Marxism.
I didn't say it was close to Marxism, I said it was one of the two closest things to Marxism that had been tried (both of which are directly attributable to Marxist influence mitigated by other forces); in fact, my point was expressly that neither of those two things was close enough to Marxism to draw substantive conclusions about Marxism from either, or even both considered together.