What is the pI and size of the protein of interest? When does the precipitation occur? When you load the sample o when you start increasing the salt concentration? What chromatographic medium are you using? What is its molecular weight cutoff? What is the green stuff made of?

 pI /  MW unknown.  I'm looking for Cd-associated proteins, which I'm locating amongst my fractions using graphite furnace AAS.

Precip appears to occur when washing with low salt buffer (20 mM Tris + 10 mM NaCl) after loading sample (5 mL wash, using 1 mL column, running at 1 ml / min).  My hunch is that this is washing out the detergent from the buffer that the sample was prepared in, leading to precipitation.

Medium is Q-sepharose HP (from GE Healthcare), MWCO - uncertain, since this is an anion exchange resin and thus not separating based on MW. Bead size of resin is 34 um.

Green-stuff - presumably chlorophyll, other pigments, and the missing 70% of the cytosolic proteins that I loaded onto the column.

If you don't use any detergent you will most likely have membrane vesicles or fragments (where the chlorophyll would be located, I assume), even after filtration because these will be too small for filtering. (Actually, one method to generate vesicles is by passing lipids through such filters multiple times).

I would consider your extract as semi-crude lysate which should be clarified by ultra-centrifugation at 100.000g. Then your membrane fraction will be in the pellet and only the "real" soluble fraction will be in the supernatant. Don't forget to remove or shear the DNA (by DNAse digest or sonication) to minimize the viscosity and have a better elution.

In case your protein of interest is in the membrane fraction of course you need to work with detergents and extract it from the pellet of the ultra-centrifugeation step. There is no way avoid detergents (and you need to test which one is working best for your protein).

You should not assume that 100% of the protein in the extract will bind to the ion exchange column. Whether or not a protein binds depends on its surface charge, the pH, the ionic strength, and whether the column is anion- or cation-exchange. Change any of these parameters and you change which proteins bind.

Instead of ultracentrifugation I have had good success with ammonium sulphate precipitation. After addition of a relatively small amount of AS (~20% saturation ) the membranes can be removed at 5000 rpm or so in big, preparative rotors. In practice, you determine that concentration of AS where your protein is just soluble, and precipitate junk there. The clarified supernatant is then brought to an AS concentration that precipitates your protein, and spun again. When correctly done, the precipitate from that step contains ~1/3 of the total protein in your lysate, but most of the activity.

With some proteins, acetone or heat work better than AS.

I agree with Englbert Buxbaum, that is exactly the approach I have used when purification of proteins from plant sources where chlorphyll's will cause interferance, in binding to the chromatography media.