Funny thing, "millimeter of mercury" is a unit of pressure, but "millimeter" is a unit of distance.
"Fluid ounce" is a unit of volume, but "ounce" is a unit of mass.
"Pound" (or "kilogram") is a unit of mass, but "pound force" (or "kilogram force") is a unit of force.
I understand the argument, it's just not a very compelling argument. Explaining the argument one more time is not really convincing. If I'm going to embark on a mission to remove ambiguity from measurement systems, my first choice would be to abolish the use of KB=1024 bytes. The "fluid ounces" and "ounces" thing just does not seem like it poses as much of a problem.
Addendum: I'm also not trying to be contrarian here, and I'm not trying to advocate for some kind of supremacy of US customary units over SI. Most countries have some form of non-SI customary units still in use and some amount of SI adoption. The SI units are preferred for lots of reasons, but it's not like the various systems of customary units are illogical or nonsensical. There's an explanation and a logic behind them, like how US customary volumetric units follow powers of 2, or how a "mile" is a thousand paces (nice round power of 10). The ounce / fluid ounce relationship is has the same physical explanation as the gram / milliliter relationship, because they are both approximations for the density of water, as a reference point. Neither relationship is exactly the density of water, because the respective units have been redefined, and the density of water is now something you look up which happens to have a value close to 1.0 with those particular choices of units. Just as the meter was originally defined as one millionth of the Earth's meridian, the mile was originally one thousand paces, and after standardization, neither fact is true.
Again, I can understand why people want to advocate for SI, but that doesn't mean that customary units are illogical or nonsensical.