Some of the core issues underlying the disagreements are as follows:
1. Those who argue that the Bullet Cluster (and El Gordo) disfavor DM are arguing from a LambdaCDM type cosmology in which cold dark matter should make such high velocity collisions vanishingly rare, when they aren't vanishingly rare. DM proponents argue, however, that this just means that the galaxy assembly process that they use to model these quantities needs a little tweaking, rather than seeing it as a fundamental flaw in DM theories or even Cold Dark Matter theories. The gravity based MOND theory based cosmologies, however, naturally produce higher expected relative velocities of colliding galaxies. See PAPERS ONE, TWO, THREE, FOUR, SIX and SEVEN in Post #7 in this thread.
The Bullet Cluster (via the Wikipedia link in Post # 7).
El Gordo (via the Wikipedia link in Post # 7).
2. The perception that the Bullet Cluster (and El Gordo) help DM vis-a-vis gravity based explanations of dark matter phenomena is an intuitive reaction to the displacement of DM effects from some masses in theses systems. One study found using gravitational lensing evidence at a statistical significance of 8σ, that there was a spatial offset of the center of the total mass from the center of the baryonic mass peaks.
See Clowe, Douglas; et al., "A Direct Empirical Proof of the Existence of Dark Matter".
648 (2)
The Astrophysical Journal Letters L109–L113 (2006)
arXiv:
astro-ph/0608407.
This separation between the center of total mass and the center of baryonic mass is generically unsurprising in DM particle theories, but it is inconsistent with gravitational explanations that share certain properties with Newtonian gravity (basically, it is inconsistent with Abelian gauge theories - compare Sections 5 and 8 at
this link, for an introduction to what that means).
But as the proof of concept papers illustrate, this perception is mostly due to a failure of researchers like Clowe, et al., to realize how non-linear behavior in non-Abelian gravitational based explanations can indeed successfully address these issues. See PAPER EIGHT and PAPER NINE in Post #7 in this thread.
3. Self-interacting Dark Matter (SIDM) theories that have a dark matter to dark matter fifth force mediated by a massive but much lighter than W or Z boson force carrying mediator particle has less well developed cosmology models to predict frequencies of relative velocities of galaxies relative than LambdaCDM. Proponents of these theories don't see these colliding clusters as a problem and instead think that they provide useful benchmarks with which to calibrate the parameter space of SIDM theories. See PAPER FIVE in Post #7 in this thread.