Do ion-exchange resins soften water through a kinetic equilibrium process?
(1) Water softeners use an ion exchange material that is reversible, so that after it has been used a while and the ion exchanger becomes loaded with calcium ions, it can be regenerated to the sodium form by flushing with salt (sodium chloride) solution. This would suggest that the affinity of sodium and calcium ions for the resin do not differ that greatly. I would doubt that either kinetic or steric factors count much here either, although a divalent ion like calcium might bind more tightly by being held electrostatically by more than one anionic group on the resin.

(2) I think the primary reason water softeners work is that they typically use the ion exchange resin in the form of a vertical column: you put the hard water in the top and soft water exits at the bottom. When hard water is introduced at the top of the column, a local equilibrium is established between ions in solution and ions bound to the resin, with a somewhat lower concentration of calcium ions and a corresponding higher concentration (at a 2:1 ratio) of sodium ions. As the water moves down the column, this equilibrium is reestablished again, but this time, the concentration of calcium is lower still. This repeats a large number of times, until all the calcium ions are replaced with sodium ions. I have heard this effect referred to as "mass action".