First, Bullet Cluster is not a problem for modified gravity. There have been numerous publications explaining why. In fact, it took much more effort to reconcile the Bullet Cluster with cdm than it did with modified gravity.
Secondly, clinging to the Bullet Cluster without mentioning Abell 520 is either ignorance or deception. Either way, there exist known celestial phenomenon (like galaxy rotation curves, the phenomenon that originally started the idea of dark matter) that are not adequately explained by dark matter theories (the same is true of modified gravity btw), and ignoring them in order to claim that we KNOW dark matter exists is intellectually lazy.
The problem with this discussion is that the intricacies of dark matter theories are much better understood by the cosmology community. Modified gravity on the other hand, it understood at best superficially by many cosmologists. As a result, whenever new findings in astronomy are published, there is a stampede of publications by people, who know dm but are ignorant of modified gravity, explaining why this "proves" once and for all why dark matter exists. The few modified gravity researchers out there are then left running around refuting all the false statements made about modified gravity.
I think Stacy hit the nail on the head with this quote:
I also agree that this [modified gravity theories] is contrived. But we are WAY into contrivance with LCDM(...). We’ve just gotten familiar with the contrived parts so that they no longer bother us. That doesn’t make them any less contrived.
My takeaway was that since the CMB spectrum seems to require dark matter, it's going to be there even if some form of modified gravity is also true. I've barely heard either side of the debate mention this in layman contexts. What's the modified gravity perspective on that?
As far as I see, one argument is that there can be multitude of explanations for dark matter, both baryonic and modifications of known laws (gravity, newtown dynamics). But the other commenter says that all other explanations besides baryonic are ruled out by data. Did I get it correctly?
That's something you don't see in physics. Ever.
There is always some alternative explanation that isn't ruled out by data. One may rule out all known explanations, but the explanation set is infinite and has a crazy topology. You can't ever exclude them all.
For me, a modification of gravity would be more aesthetically pleasing than dark matter, but that does not appear to be how Nature has chosen to be.
All the commentators agree on this. What Ranier and Stacy are pointing out is that the same thing is true of LCDM. Dark matter does not do a good job of explaining galaxy rotation curves (even though this is the context which dark matter was originally proposed for), bullet cluster, abell 520, or lots of other galactic dynamics.
Of course, MOND has its own share of problems. Most importantly that Sean points out is the 3rd peak on the CMB. Stacy sounds like he's holding out for the possibility that relativistic formulations of MOND may explain this peak, though he admits that may not happen. To support his position, Stacy makes reference to other instances where MOND had unintuitive but correct conclusions (like for the bullet cluster).
Basically what these are saying is that if the universe (and space around galaxies) is expanding, then stars would be dragged along with that expansion and move outward from the center of mass if they orbited at their expected Newtonian speed (they would gain potential energy as their "altitude" increases).
I'm wondering if this energy didn't go into the star (because it would violate conservation of energy to see a star moving faster and faster over time) then maybe the energy goes into space itself, showing up as "dark" energy, which has gravity by mass-energy equivalence. So basically the farther away we are from something, the heavier space appears in that region from our frame of reference. Or maybe the extra speed of distant stars has more to do with how long they've been pulled by the expansion of the universe than how much mass is near them. That could maybe explain the pictures of colliding galaxies that have uneven distributions of matter and dark matter that we don't see in individual galaxies. And why we're unlikely to detect dark matter as a particle locally (because the expansion of space is more easily observed over large distances).
I guess one way to prove this theory would be to look for unevenness in the Hubble constant (red shift), which would mean an unevenness in how fast (or how much) space is stretching in different regions. The last link seems to agree with something along those lines.
Anyway, I'm not a physicist, just throwing ideas out there! Feeling kind of embarrassed to post this layman's analysis but what the heck.