I reached the isle (as a member of the guild already) one day and just couldn't walk towards the obvious exit listed (east). What's up?

Did you ever ask the elf for your reward? ;) Do the quest again and try that.

I went there yesterday after having left for the mainland.

Obvious exit: east
>east
There is no obvious exit east.

That is what happens.

I am not allowed to go past the docks at Eil-Galaith while I have already done that before (after leaving and returning)

I was able to reenter but not sure what I am doing wrong yet. Probably not a bug or something so excuse me and disregard/delete.