What does "not to betray too green an interest in fate" mean?

Can someone help by paraphrasing this sentence from Thoreau's Walden:

Think, also, of the ladies of the land weaving toilet cushions against the last day, not to betray too green an interest in their fates! As if you could kill time without injuring eternity.


Oxford has an interesting alternate definition for green.

Still strong or vigorous: first there was green old age, hardly different from middle age

See definition 3.5

It seems like it might be synonymous with keen.