As the title says, if you are not on the same realm as the guild you are in, you cannot access the guild bank.
We have troubleshooted possible other issues such as ranks and other players to find the cause of it and have concluded it is because of realm affiliation.
I (Tarren Mill-EU), cannot access the guild bank (Kazzak-EU), neither can anyone else who is of a different realm (tried Argent Dawn, Ravencrest, Tarren Mill) those of us on other realm (not just myself) have no access to the guild bank. We do have access to guild repairs, so that part is working. But the ability to view, withdraw or deposit is unavailable to us.
Although not a problem so much now, when the new raid tier comes out, most guilds will deposit consumables within the guild bank for their raiders to use during progression. This will not there for those of us in different realms to the main realm. Albeit it a mere inconvenience in needing to either provide our own consumables, or being made to trade between each other in raid itself, its still a bug nevertheless.