How to filter out magnesium acetate (a soluble salt) quickly and cheaply from water
Ion-exchange resin can be made with $\ce{H+}$ cations on one type of resin and $\ce{OH-}$ anions on another type of resin. These would leave the water without the any of the magnesium or acetate ions effectively without replacing the ions with other ions. This is how we deionize for general chemical use. This happens according to the reactions below:
$$\ce{2HSO3R + Mg^{2+} + 2C2H3O2- -&gt; Mg(SO3R)2 + 2HC2H3O2}$$
$$\ce{R4N+OH- + HC2H3O2 -&gt; [R4N+ +\ C2H3O2^{-}] + H2O}$$
In these examples, the sulfonates/sulfonic acids and ammonium cations are tethered to the resin so that they can't dissolve.

The downside to this is that if you are trying to measure something else in the system, if it is ionic, it will be removed as well.

I've never had to source ion-exchange resin myself, so I'm not sure of the easiest way to go about it. There's pleanty of deionization resin on Amazon. The mixed stuff is simple to use, just mix it with your water, agitate for a while and then filter it out and you'll have removed all the ions. That is expensive, though, because it's single use. 

You can also buy regeneratable ion exchange resins. You don't want to mix the regeneratable stuff, and you have to do two separate ion-exchange steps, one with the cation-exchange and one with the anion-exchange. It's pretty easy to regenerate, though, as far as I know. You just use strong acid with the cation-exchange to redissolve the soluble cations and use a hydroxide solution to regenerate the anion exchange resin. It can't be done forever because there are some cations and anions that just won't want to redissolve, but if you're doing it a lot, might be worth it. I can't seem to find the anion stuff except in bulk.

I'm guessing the mixed type would be more appropriate for most applications. If you really need it quickly, I think you can buy the filters at Lowes/Home Depot and just run it through those or open them up and get the resin out.

Update: These filters are the only ones I saw that said they actually have the "dual ion-exchange system." Their website actually says it gets down to "000 total dissolved solids," which is pretty impressive relative to other water filters from what I've seen (depending on what "000 TDS" actually means).