I. What puts you off in a faction? (iRP and ooRP)
Pretty much what Ramke stated. But also what I personally consider a lack of creativity (this only applies to some factions obviously). It's killing fun when half of a faction brings the very same attitude and gameplay style, you know. Yeah, pretty much ooRP and inRP lack of creativity. That goes for interacting with said faction or playing in it.
II. What makes you log and long for faction interaction? (iRP and ooRP)
RP with members. RP with allies. RP with enemies. RP overall, PvP aspect as a result is fine, not necessary (but still fun). Oh and also piracy, for some reason it never lost its magic to me, so I sometimes yearn for raids and lockdowns. (And my positions. I feel like I am expected to log with the ranks I bear within several factions.)
III. Specifically, would you care to interact, support or play in a faction that specifically goes for supplying underdogs with at least an inch of morality?
It's one of the possible things doable as GC, as a side thing. I did it before, it was fun and I would gladly interact and help out everyone who wants to do this in a larger scale. Wouldn't be able to play for it though, probably wouldn't be able to give that faction the love it deserves then.