Mrs. Steward's bluing.

Bluing the whites is as old as ever. If I am not mistaken, the whitening properties of this colloid was discovered by accident when a "piece of blue" fall in one of the batches where paper was being made ions ago

Body oils cause the discoloration, they attract dirt and trap it. Try soaking in borax or Biz then double rinse it. If the dingyness comes out but it is still kinda drab put a few drops of blueing in the rinse water, mix well then add the blanket, run a long rinse and long spin dry. My mom was a dry cleaner.

I thought this was a racist thing.

Dim the lights.

Fels Naptha!

Why don't you dye it blue?

Lol maybe dye it another colour as it's your only real option.

Soak it in the bathtub with OxyClean powder and hot water, for at least an hour.
Then launder with OxyClean and detergent. Again, in hot water.

Try white vinegar. Look up the cleansing properties of the stuff.

Bring it to a dry cleaner?

As previously said Borax or in its refined form Boric Acid. Bleach will only make whites containing Polyester or Nylon a worse cream. Most stain removers will also not help and Oxygen rich detergents will also cream the Polyester. Borax from supermarket or hardware, Boric Acid from your industrial chemical store. both are cheap and you don't need much

Try using a stain remover. I had some oil on one of my favorite pairs of pants. It had not come out, even after several washes. In a last resort, I tried a stain remover gel, let it sit overnight, and washed. Oil gone, pants usable again.

Spray and Wash, but let it set for awhile. Bleach would b my first choice. Oxyclean works on some stuff.

It seems all white fabrics over time get discolored, primarily through minerals in the water when washing. This is especially true with well wter which discolors whites much faster.

You might try dry cleaning, which uses chemicals to clean and may disolve the bond of the minerals, bot even that may not work. Other than that, you may hve to buy a new one.