Going somewhat in reverse order...
The Honored Matres no longer have melange, but have another drug, a stimulant, which they use to heighten their own powers. It's also made clear that they don't have Other Memory or other Bene Gesserit capabilities that rely on conscious control over ordinarily unconscious mechanisms, all of which are unlocked by the Agony. Instead, it is strongly suggested throughout Heretics of Dune and Chapterhouse: Dune that the Honored Matres have channeled their powers almost entirely into unconscious avenues -- planted compulsions, violent reactions not mediated by a central nervous system, and of course the use of sexual addiction as an unconscious tether on others. There is no indication that the Honored Matres go through an "agony" process in the same way that Reverend Mothers must.
The Fish Speakers also never went through the agony. In fact, it's implied that they consume spice exactly once in their lives, and only if they actually attend Siyanoq. The spice in the wafers triggers a state more like the Fremen "spice orgy" than the agony, creating a tau in which everyone present shares with each other and with their God Emperor. It is not enough to addict them, or even prolong their lives, let alone give them access to Other Memory.
It is not clear in Chapterhouse: Dune whether Rebecca is unique in Secret Israel, or whether the Jews of that future commonly have "wild" Reverend Mothers in the same vein as the Fremen. It is even less clear where the Rabbi got hold of the necessary spice essence to allow Rebecca to attempt it, since all of that happens before we meet the characters! All we know is that Rebecca has done it, and that she and the Rabbi knew exactly what they were doing, in emulation of their sometime-allies, the Bene Gesserit.
[It is fairly plain that it was spice essence and not some other poison that was used, since it's made explicit that Rebecca is a spice addict, complete with Fremen-blue eyes, as a result of her transformation.]
Finally, of course, we have the Fremen. In the novel, Dune, it is somewhat ambiguous whether the Fremen Reverend Mothers are directly "descended" from a Bene Gesserit Reverend Mother, or merely acting in imitation of them, having somehow learned about the agony. It's even possible that the reverse is true -- that the Bene Gesserit discovered the utility of melange essence to induce the Agony, as opposed to other poisons, from the Fremen.
We do know that the Missionaria Protectiva had been among the Fremen, and that the Fremen are good at finding things out. We also know that, in the novel, the existence of these "wild" Reverend Mothers is not commonly known, even among lay sisters of the Bene Gesserit -- Jessica was surprised.
[By contrast, both the 1984 movie and the 2000 miniseries simplify matters by making it seem that Reverend Mother Ramallo is actually Bene Gesserit herself.]
Beyond this, we have no canonical evidence to state categorically that other groups undergo a similar process to unlock Other Memory. The Tleilaxu, of course, use the ghola process to perpetuate personal memory, and through Duncan Idaho even unlock an ability to recover access to memories that shouldn't be physically present in the cells involved, but that's different from a Reverend Mother (or Kwizatz Haderach) accessing Other Memory.
On the other hand, there's nothing that rules out that another group, particularly out in the Scattering, might be doing so. Herbert is at pains repeatedly to try to depict the magnitude of the Scattering and the many different paths humankind might be taking. Certainly, if both the Fremen and Secret Israel have figured out the secret, it suggests that others could. However, no explicit mention is made of such a group.