KIBM RNAV (GPS) 10 -- did I find a charting error, or what is the TERPS rationale for this?
This is speculation, but in the absence of an obvious technical reason it's at least possible that this is because category C/D pilots have better lobbyists than category A/B ones.

I found an interesting but somewhat dated (1995) document  called Establishing Visibility Minimums; the author used to chair the ALPA TERPS committee. It says:


  [The TERPS concepts] are a combination of science and politics, with a
  lot of undocumented historical precedence thrown in for good measure


And:


  The political horse-trading that led to the 1976 [TERPS] revision [...]


In other words, we shouldn't necessarily assume that rules and regulations are entirely based on well-defined and documented technical criteria.

The (now outdated) 1976 chart in that document shows a default minimum of 1 mile visibility for all categories (with the single exception of an ILS with DH of 200', which is 3/4) or 1/2 with approach lighting, so a 7/8 minimum is a more recent change. So you could ask, why was this change made? One way would be to find the NPRM or other public records that detail the reasons for the change, but in practice it may be easier to contact the FAA directly and ask them (possibly under the FOIA if the information isn't already public).

One theoretical possibility is that the airline industry successfully lobbied to have 'their' minimums reduced in certain circumstances due to better training, equipment or whatever, and this approach is one of the affected ones. Diverting airline flights is enormously expensive, and the industry has a large incentive to make sure that as many instrument approaches succeed as possible. If lowering the minimums by 1/8 allows even a few flights a day to start an approach that would otherwise be illegal, that could add up to a huge financial saving.

But this is entirely guesswork on my part, I just wanted to make the point that sometimes we look for a technical explanation where the real reason is financial or political. For a definite answer, I would ask the FAA directly.