True, but it does seem (at least to me) materialism is moving closer to idealism than idealism moving closer to materialism.
I was going to bring this up in the other thread when you asked about information theory but that thread was just too much of a cacophony. When Darat started this one I thought that might be the time to bring it up and expected some discourse. Basically I'm just swinging at the fence anyway and even if I foul out at least someone might get conked on the head.
Well if I was interpreting your earlier posts correctly you suggested that the information of an object was not the object itself. If I can draw a parallel, a cogent model is developed from experimental data collection of an object, but the model is not necessarily the object itself because it's an abstraction. I would have interpreted you and nonpariel discussing observation data and modelling.
The data is the information of an object, the model is an independent abstraction developed from the data. It sounds weird to parse "independent" and "from the data" however good models should be able to function with each other. If you were to model from the information of many object's information and the models all function with each other they're still abstractions and independent of the data; their dependency with each other is all that matters)
Now, the wrinkle from the Mathematical Universe proposal is that if we did model all information in the universe and we suppose that this information is "reality" then the models being abstract seems semantic. That wrinkle is what I am interpreting leads you to say that materialism seems moving towards idealism.
I would say however that if we were still moving materialism somewhere, it wouldn't be towards idealism. Let me say right about here that everything about information and modelling that I've said above is not really influential to either materialism or idealism since both can interpret information equally well. Materialism suggests no distinction between reality and experience; even "consciousness", whatever it is, is not abstract. Idealism (I'll stick with the monastic concept as Bernardo Kastrup suggests instead of dualistic) suggests that conscious experience is reality which necessitates that data requires consciousness (again, whatever it is).
Materialism with regards to information do not move towards this monastic idealism; that kind of monastic idealism has no ability to interpret or discriminate information to establish itself as conscious, much less reality. Deepak Chopra has this problem in his monastic idealism philosophy (one that Bernardo shares).
But there may be a funny issue that goes back to the mathematical universe wrinkle. If the abstract mathematics are no longer abstract since they model all information then "abstract" is semantic. One may wonder if monastic idealism also becomes a semantic philosophy.