It looked at first as if an Eco-Friendly Word is one that
shares at least one letter with the word GREEN
but as Volatility kindly pointed out in comments when I proposed this
LANDFILL, which contains an N, is explicitly labelled as a non-Eco-Friendly Word
so this couldn't be right. Still, something along those lines seems likely. So, if the lists in the question are correct, then
(within those lists) letters BEGHMRU are found only in EF words, letter F is found only in NEF words, letters ACDILNOPSTVXY are found in both sorts of word, and letters JKQWZ are found in neither. If EF words are exactly those containing at least one letter in a certain set S, then S must contain G (because GAS contains no other letter not also found in NEF words); it must contain E (because despite its length EXTINCTION contains no other letter not also found in NEF words); and if it contains those two then all EF words in the list are covered. So S must include G and E and must not include any of ACDFILNOPSTVXY; it may also include some or all of BHMRU and JKQWZ. So, e.g., we could say that EF words are exactly those sharing a letter with BUGGER or GEM or HUGE or EMERGE or HUGGERMUGGER.
If anything of this sort is right then
perhaps the most plausible is HUGGER, as in "tree-hugger". Unfortunately there are lots of Ts in NEF words, so the answer definitely isn't that an EF word is one that shares letters with TREE-HUGGER.
Of course another possibility is that
an EF word is one that doesn't share any letters with some other word. We might hope the word in question had some anti-environmental significance. Alas, the only letters we could possibly form that word out of are FJKQWZ and I don't think there are any suitable word (or any words at all) formed from just those letters. Fjqk!