Victor,
The reason behind the similarities in the Hoffmeister series and ion exchange selectivity stems from the common elements affecting both of these properties: hydration (as mentioned above by Hans). Hoffmeister's original publications dealt with the effect of different electrolytes on the solubility of eggwhite proteins. Unfortunately, I haven't been able to lay my hands on the original publication (there was a series of papers published in the 1890s) so I can't elaborate on the details of his experiments. But, if one considers the effects of different ions on the solubility of the proteins in aqueous solution (without using such a high ionic strength that the proteins are salted out), then the tendency of the ion to result in a water insoluble protein salt is connected to the extent of hydration of the ion producing a salt with the protein. The lower the hydration of the ion, the lower the solubility of the protein.
In ion exchange, to a first approximation, the driving force is quite similar. Highly hydrated ions (which more effectively become incorporated into the water structure with minimum disruption of the water structure) prefer to stay in the external solution outside the ion exchange material while poorly hydrated ions (which are minimally incorporated into the water structure with maximum disruption of the water structure) prefer to be in the ion exchange phase. Of course, in the case of ion exchange there are other factors providing the secondary retention mechanisms which can cause significant deviations in selectivity from the Hoffmeister order. For example, there are ion exchange materials capable of generating all of the following elution orders: bromide, chlorate, nitrate; chlorate, bromide, nitrate; bromide, nitrate, chlorate and chlorate, nitrate, bromide. Although I was never able to determine unambiguously what the Hoffmeister order is for this set of anions (a search of the published literature reveals at least six different Hoffmeister orders, but I have no way of knowing if any of them are the actual order in his publications since I was unable to obtain copies of the original publications), it's safe to say that the Hoffmeister order would be only one of these orders.
In general, differences in selectivity between ion exchange and protein solubility are connected to differences in entropy and enthalpy of hydration. For species in solution, entropy of hydration tends to be the dominant factor. For cross-linked ion exchange materials, enthalpy of hydration tends to be the dominant factor with the extent of cross-linking influencing the relative effect of enthalpy and entropy.