Really, I think that outside of scientists of a rather 'religious' stripe we got there already. Theories of meaning like those of Lacan and Desassure already work in this way. We are used to them.
All experience is intersubjective negotiation. You can attempt to ensure agreement by modelling the view of the other subjects in triangulation, but you cannot fully capture or predict their experience in detail. What is shared is also shaped by the process of observation, and you can only get so close to the perspective of someone who is viewing something that is changing at the same time.
It is not really hard for us to take in this mutualized, psychologized notion of language. It is almost impossible, and utterly unproductive, to avoid falling back on more absolute models for efficiency, but the problems of dealing with other people in all their psychodynamic complexity make the case that this is far closer to reality than the models from which we work on a regular basis.
Why is it somehow seen as almost impossible for people to use this picture of our shared mental reality in the context of our shared physical reality?
But as for figuring out what the effects are, they are the same effects already uncovered by modernist collapse in psychology, though with a deeper, more inescapable texture: the problems of Sartre, Wittgenstein, Nietzsche and Lacan. The model is not new, it is simply more thoroughgoing than we might have imagined.