According to the SEP:

Undaunted, von Neumann and Birkhoff suggested that the empirical success of quantum mechanics as a framework for physics casts into doubt the universal validity of the distributive laws of propositional logic. Their phrasing remains cautious:

Whereas logicians have usually assumed that properties … of negation were the ones least able to withstand a critical analysis, the study of mechanics points to the distributive identities … as the weakest link in the algebra of logic.

In the 1960s and early 1970s, this thesis was advanced rather more aggressively by a number of authors, including especially David Finkelstein and Hilary Putnam, who argued that quantum mechanics requires a revolution in our understanding of logic per se. According to Putnam, “Logic is as empirical as geometry. … We live in a world with a non-classical logic”

We don't have to go to quantum mechanics to show how a non-classical logic works. For example, the calculus can be done, relatively intuitively via intuitionistic logic. One of their main results that all functions are smooth! Given, how little this quite remarkable mathematics is known, even amongst mathematicians, I don't hold out much hope for a radical envisioning of how quantum mechanics is taught, never mind looking at alternative, and better foundations - though, one can hope.

One point, worth bearing in mind, is that Newton advanced both his theory of calculus and gravitation at the same time. So its, most likely, when change does come, it will come from more than one direction, that is from both geometry and physics.

Another point, also worth bearing in mind, is the sociology of physics (or rather - physicists), their inate conservatism (most of them are not great, radical thinkers). The people who most trumpet quantum mechanics and relativity, are likely to be, the ones, at the time of Einstein and Dirac, to have been trumpeting classical physics and not the new, radical phyics. Now of course, that the dust has settled, and they can see which way the picture is pointing, they're all for it.

But that isn't the main point I want to make. It's a question of numbers, in Wigners day, physics was more or less a gentlemans club; today, it's an industrial-sized battery-farm, battery-farming physicists, with about (ahem), the same lack of real physical or mathematical understanding as perhaps, one might understand battery-farmed hens, have (that might be a bit strong, but you get the point). Thus, even when a change is possible, its merely being held up by numbers, and by conservatism.

Relevant sources: Putnam's later article A Philosopher Looks at Quantum Mechanics (Again) indicates Michael Redhead on quantum logic as the original source of the repudiation. That article though I don't have access to.

– Noah Schweber – 2020-01-23T22:34:57.873You should know that Hilary Putnam changed his opinions radically and often, and is famous for doing so publicly (e.g. on realism in 1970s). But the disappointment in "quantum logic" was (and is) very broad, Putnam simply followed the mainstream. The analogizing of the Hilbert subspace lattice to Boolean algebra ("logic") just isn't too fruitful, and adding quantification even less so. Some issues were discussed on Math SE.

– Conifold – 2020-01-23T23:50:37.287Maudlin has a paper detailing Putnam's evolution on quantum logic:"

Early in his career, Hilary Putnam believed that modifications of classical logic could both solve the measurement problem and account for the two-slit phenomena. Over 40 years later he had abandoned quantum logic... The trajectory from Putnam's earlier views to his later views illustrates the difficulty trying to solve physical problems with alterations of logic or mathematics". – Conifold – 2020-01-24T00:17:23.037@Conifold in one interview in 2012 (4 years before his death), he said "I think I agree with just about every paper in my first two Cambridge University Press volumes, if not with every argument". Do you know what papers is he talking about? Are any of these papers related with the subject of Quantum Logic? – stifenahokinga – 2020-01-26T20:47:21.870

@Conifold link: http://www.harvardphilosophy.com/wp-content/uploads/2012/09/On-Mathematics-Realism-and-Ethics-Hilary-Putnam.pdf

– stifenahokinga – 2020-01-26T20:47:44.737Volume 1 and Volume 2. Blanket statements of this sort are not meant literally. Maudlin cites every paper of his remotely related to QL. – Conifold – 2020-01-27T01:23:56.817