Druids (or maybe paladins) only guild in WoW. Possible? Even for ultimate PvE and / or PvP?
Back in the very early days of WoW my raiding guild had loads and loads of Paladins. They staged a raid on Molten Core that was 40 Paladins once, just for fun. I think they did pretty well. as I recall they got to at least Baron Geddon before wiping and may have possibly beat Shazzrah. This was when the level cap was 60 and before even Blackwing Lair opened.
I'd say a PvP guild would work just fine, you'd just have to adjust tactics and make sure you've a variety of specs to cover the different roles.
There really is no way to keep opinion out of an answer to this question, so... 5 man dungeons would be possible with an all druid or all paladin group, but it would be very difficult to be successful in a 10-25 man raiding environment.
Most encounters are designed with certain class abilities in mind. Ex. Heroism/Bloodlust (From a Shaman) or Time Warp (From a Mage). I am not saying that an encounter would be impossible without those abilities, but they become easier with them.
Also, most raid fights require a healthy mix of ranged and melee dps. With this in mind, Druids can be both melee and ranged dps but Paladins are stuck with only melee.
As far as PvP is concerned, it depends on what you are doing. 10 man rated battlegrounds? You would probably not fair very well against a team with a mix of classes because of what different classes bring to the table. Paladins have some major drawbacks in PvP situations, they can be kited way too easily and they really have no true CC (Crowd Control) for peeling and assisting teammates.
Back when Cataclysm first came out there were a few five man arena teams with four Retribution Paladins and one Restoration Shaman. Their tactic at the beginning of the match? The Shaman would use Bloodlust/Heroism and the Paladins would use Avenging Wrath with Hammer of Wrath and just nuke down one or more enemies before they lost one. This group was broken when Bloodlust/Heroism/Time Warp were removed from arenas.
TL:DR - Is it possible to have only all Druids or all Paladins in a group or raid? Yes it is.
Will it be as easy to be successful at what you are trying to accomplish? No it wont.
I am a strong believer in "Bring the player, not the class" however, and what I say is, do whatever makes you happy and helps you enjoy your time playing World of Warcraft.
I'm a paladin myself and I genuinely think that an all paladin guild could work (to a point). The reason for this is that paladins can spec to fill any of the roles (tank, dps, heal) because of that you would have an all paladin guild that could be very versatile and useful in comparison to any other one class guild.
However this has some pros and cons. Pros, Paladins can use plate armour and can heal themselves regardless of spec. Cons, Paladin healers are by far the weakest healers and can struggle in raids and paladin tanks are second best to warriors and to make matters worst it often takes time for paladin dps to get into full swing (buffs like inquisition etc.)
Overall though paladins are the best choice for a one class guild but you'll struggle with high level dungeons and raids because paladins are too versatile to do one job extremely well so don't expect too much.