Let me start with a big picture. Obviously the empirical consensus at present is the standard model coupled to general relativity, with a dark sector and neutrino masses too. If you are looking for a theoretical consensus beyond that, that will always be controversial, but there is a specific big picture that exists. It's basically the string theory landscape, the set of all string vacua, something which is explored most deeply these days by the "swampland" program which seeks to identify what kinds of low-energy physics can't show up in quantum gravity.
The reason I mention string theory as the summit of consensus, is that it naturally subsumes a lot of other theory-building that followed the gauge theory revolution of the 1970s. Grand unification, supersymmetry, supergravity, they all embed naturally into string theory. There have always been people following other paths, none of these unification ideas have received empirical confirmation, and these days the skeptics are buoyed by the intellectual component of the rising tide of western populism, so who knows where things will be in future.
But this framework exists and it gives us a solid point of reference if we want to know the prospects of a particular idea. So we can ask, where does "noncommutative" physics fit into this? Here we should make a distinction between the school of noncommutative geometry associated with Alain Connes, and all other approaches, since the school of Connes et al is by far the best known and most distinctive approach of this kind.
As far as string theory is concerned, I would point to two things. For noncommutative field theory, we have that it can arise as the "worldvolume" field theory on a brane; and for noncommutative gravity, Tamiaki Yoneya's space-time uncertainty principle is the way in which noncommutativity of space-time coordinates was discovered within string theory. But what I would say is that neither of these appears to be of phenomenological interest in string theory. Like Hawking radiation, they are theoretical phenomena which are not expected to ever actually be observed. No doubt someone has proposed circumstances in which they are observable, but in general they are not part of what string phenomenologists study.
Now, how about the Connes school of noncommutativity? Here I particularly mean the "noncommutative standard model". That has developed more as a rival or as an independent would-be theory of everything. But there is an interesting comment right here on Physics SE, made by Urs Schreiber, who works on string theory but has a few eclectic tendencies, in which he speculates as to how the Connes paradigm of noncommutative geometry could be viewed as an approach to the particle limit of geometric string vacua (I say geometric because string theory contains "non-geometric" vacua too). Urs has a reference or two to bolster his claim, but overall says that the two research communities haven't really communicated, and I can't see that that has changed in the decade since his comment.
OK, so much for a string theory perspective. I would add that from the perspective of the earlier stages of this mainstream synthesis, like grand unification, noncommutative geometry is basically absent as a consideration. Everything is ordinary field theory, then once gravity is involved it's string theory.
What about the Connes school on its own merits? How does the noncommutative standard model fare as an independent research program? In the lead-up to the Higgs discovery, Connes made a confident prediction that the Higgs mass would be 170 GeV, which was falsified a few years before. Then afterwards they added an extra scalar (or rather said that they had found this extra scalar already implicit in the model), and that this made a range of masses possible, that includes the observed mass.
I am not actually sure how the formalism used in the noncommutative standard model compares to the ordinary field theory approach to the standard model, e.g. is it provably equivalent in some areas? Is it capable, from its own axioms, of generating or motivating all the approaches, perturbative and nonperturbative, that have had empirical success? And then there's the gravitational part of the NCSM - how does that look from the perspective of the usual questions about quantum gravity, such as non-renormalizability and UV-completeness? I have seen both skeptical and interested remarks by outsiders - Urs Schreiber's post is an example - but I'm not aware of a really rigorous comparison or "audit" of what Connes et al have been claiming, by someone who is expert in the mainstream theory.
So, that's noncommutative geometry within string theory, and noncommutative geometry according to Connes et al. I believe there may also be a variety of independent attempts to apply noncommutative geometry to quantum gravity; and I suspect that research programs involving "quantum groups" may also deserve a mention. But I have nothing to say about all those. I will add that there are a few papers out there on a non-associative approach to quantum gravity (see Richard Szabo), which claim a relationship to M-theory, so you may want to look up those as well.
