Unfortunately you're missing the thrust of Hossenfelder's developing argument: in upgrading MOND to a full relativistic theory, you necessarily seriously blur the difference between "modified gravity" and "particle dark matter".
There's some meat on this in the comments on that blog page, notably the point raised (and her subsequent reference to it) by "M_Malenfant".
Essentially her point is that when you relativize some theories of MOND (detailed examples in Famaey & McGauch https://arxiv.org/abs/1112.3960 section 7) you are inevitably adding a field to the existing fields. Whether you put it on the right or the left of the Einstein Field Equations is a matter of personal taste. The thoretical requirements however are that the field couples with matter somehow (even just gravitationally), just like the particle dark matter case (where particles may interact weakly or even just gravitationally). Moreover, when you have a dynamical, relativistic field like this, you tend to think of how to quantize it, which typically means particles as the field content and particles mediating the interaction between that and the field content of the Standard Model.
So, as she says, perhaps it's more a question of sociology than mathematics that splits particle dark matter theorists (solving cosmological problems like the details of the cosmic microwave background and its neutrino equivalent, or solving problems with the Standard Model like the QCD strong CP problem) or from modified gravity theorists (solving velocity curve problems). At some level, almost all of the still-viable proposals for these and related problems boil down to adding a field on curved spacetime.
On the other hand -- and this is where Hossenfelder (among others) deserves some credit -- this wouldn't have been quite so obvious ten or so years ago, let alone in the early 1980s when Milgrom began developing MOND.