Good answers, folks. Miami and others have identified the thing I was looking for:
A cation binding DI resin, either a single such bead in a mixed bed, or a whole canister of such beads together.
1. I don't dissolve in water when reefers use me
DI resins do not dissolve.
2. I love calcium
A cation binding resin will bind positively charged calcium to the fixed negative charges on the resin, and release H+ in the process.
3. I hate chloride
Chloride will not bind to, and in fact will tend to be repelled by the negative charges in a cation binding resin.
4. My insides are more acidic than anywhere in a fish.
When not depleted, a cation binding resin is very acidic inside. The effective pH would be below zero. The fixed negative charges are typically sulfonic acids, a very strong acid which allows all of the associated H+ to be swapped out for cations. Fish Stomach pH can drop to about 2. Some may be lower, but no animal has any pH regions below zero.
I discuss much more about how this works in this article:
Reverse Osmosis/Deionization Systems to Purify Tap Water for Reef Aquaria by Randy Holmes-Farley - Reefkeeping.com