Some one on here suggested using Murphy Oil Soap to clean up plastic handles that have that milky film growing on them.

I have quite a few tools with this condition and in the past tried a few different products to clean them off. Nothing really worked well.
So I figured that I would try the Murphy Oil Soap on a few test specimens.
I could have sworn that my wife had some stashed with her cleanings products and I had planned on "borrowing" it but I didn't see any.
I went to the store to get some but found that apparently a couple of years ago they changed the formula and now sell it as "Murphy Wood Cleaner". It's a thick gel (much thicker than I remember it being).

I used it straight out of the bottle letting the handles soak a few minutes in it. Then started by gently scraping the film off of the flat areas with a scrap piece of plastic and the grooves with a wood toothpick. After that I rinsed with hot water and dried with a shop towel. A couple of the handles needed another round of cleaning.
The result is that all of the previously milky, almost white handles cleaned up great.
I am going to keep an eye on them to see if the film starts appearing again.

Cool!

I wonder if it is the same formula? They sold a spray also that was watered down? I bought it by the gallon, it worked so well on a old walnut cupboard that was in a dirt floor basement, the back made up a side of a coal bin. Canned foods (mason jars) were stored in it and leaked. Oh it was horrible to say the least. It took a couple of hours but while it was sitting in the sun drying  from being cleaned  a person offered me twice as much as I was going to ask for it. They were happy I was happy.I will have to try it, nothing else seems to work....

The original Murphy Oil Soap is still available on Amazon.

I have always cleaned the wooden parts of my tools and anything else wood with it.  I put a blob or two of the full strength stuff in a bucket and dilute it with hot water.  Then wash and wipe.  I used to rinse, but dont bother with that anymore.  The only thing I do not use it on would be a really expensive tool where I was worried about the grain raising (plane or rule).  Using the warm water and putting it out in the sun helps it dry out quicker.  I follow up with tung oil.

Murphy Oil Soap did come in about a pound jar.  It had a jelly like consistency. 
Is this the blob you're referring to John?   I'd like to find some of the original since I'm out.
You mixed it with warm or hot water & it cleaned almost everything well.  I always used it on all of the vinyl / plastics in my cars & most nonmetallic items.  I A few years ago, the premixed liquid version replaced it around here. 
Another great thing about it is that it rinses off without leaving a residue.

I have a thought, used Snap-on screwdrivers for 15-20 years daily in the shop.  Never had that white stuff occur.  Took one home, within 6 months, sitting in my home box turned real milky, then the handle split.  My thought is the daily coating of oil, grease, and body oil from my hands keeps handles treated.   Like an old car,, they have to be used.   My ACE and Proto screwdrivers from the 50s-60s show no change from year to year.    Now some older Craftsman are getting the white stuff.

I did a small phillips head driver to see how it works. I can say spraying is not the way to go. I'm thinking a  small tub or jar fill it to cover the handle, start small add more for larger ones. Wonder how long it will last? only time will tell...       I did use a small wire brush to clean the grooves, they were filled with fuzzy stuff.

I'm trying this one too. I have at least 6 different screwdrivers with this issue. I am using a pint Mason jar to soak the handles. I think soaking them overnight is working the best for me. A few of them I have had to give a second 3- or 4-hour soak and they are clean. Like the others have said I hope it lasts. I purchased a bottle of the concentrate, and I mixed it about 1/3 Murphy's to 2/3 water.

Use hot water to get the soap working better.  Been using tooth brushes to get into the grooves.   Really scarred ones clean up with 4-0 steel, not perfect but look better.

If you leave them soak long enough all I have been doing is wiping them off with a paper towel, don't have to scrape anything. The first one I did I had to scrape and get into the small areas, then I left them in overnight and it was basically just wiping them off.

Nice work!

According to the SDS, Murphy's contains citronella oil and sodium hydroxide. The lye - being basic - probably does alot to neutralize the acidic residue that causes alot of the acetate handles to chalk and break down.