I decided to make my own cutting board out of a nice piece of black walnut I came across. It looked great before I added oil, but after I added hemp oil to one side, the whole board turned greenish. I then added coconut oil and beewax on the other side and it also turned green! The only clue I have to this mystery is that the wood (while it feels and looks very dry) was only felled from the forest about 3 months ago and stored indoors. Could the problem be wet, uncured wood?
It would interesting to see a picture of the board to help diagnose what the problem is. However, like Graphus said it is very unlikely that the boards have been properly dried after only three months without using a kiln, especially if it was stacked indoors. Most wood properly stacked and stickered will take at least a year to air dry. Moisture meters are a great tool to help discover when wood has reached a good dry state.
Now why it actually turned green, you didn't say if the green was immediate or if it took a little while, but I get the impression it was pretty quick because one side turned green before the other side even got it's finish. I've seen many walnut boards that can have a rainbow of colors from green to pink and purple. This is generally from older trees that started to decompose in the middle. Fungus and bacteria can do all kinds of colorful things to wood, and by sealing it with a nice finish might be just enough to make the colors pop.
Of course if the green came a bit later then it is likely that the moisture content help a fungus grow. If the former (color just popped) then a good seal should be enough, if the later, I probably wouldn't use it to prepare food.
I don't know why the board turned green or greenish, but I think I can definitively state that the wood isn't properly dried, or seasoned, and shouldn't have been made into a cutting board yet.
As a rule you work wood 'wet' — also called green wood, not because it is green in colour — or you use it after it is fully seasoned, which is either after a long time drying naturally (air-dried wood) or a much shorter time being dried in a type of hotbox or oven (kiln-dried wood).
I believe @bowlturner is on the right track for the greenish color.
Spalted wood, wood that has been slightly decomposed by fungal activity, is often bluish or greenish - ex: blue pine. Fungal growth only occurs in moist wood. So the wood was not allowed to dry, drying was retarded and the fungus got a foothold.
If bowlturner does as his name implies he's probably made bowls from spalted wood.