So much so that Blizzard has announced that in a future update, one of the changes that they will be making is to allow players from both sides to come together and form premade groups that will basically allow them to take part in raids together. This means that if you have a friend playing on the opposite faction, you could team up with them for raids or dungeons.
Lore-wise, it actually makes a lot of sense because more often than not, the main antagonist of the raids in most expansions tend to be faction neutral, or someone from a faction “gone bad”. For example there was Deathwing in the Cataclysm expansion who is from neither faction, the Lich King (who was formerly an Alliance Paladin) from Wrath of the Lich King, then Garrosh (the son of a main Horde character) in Mists of Pandaria, and so on.
Usually the storyline involves both factions coming together and working towards the greater good, so having a raid or a dungeon crawl that lets both sides play together makes sense. There is no release date for this update yet, but it’s something that players can look forward to in the future.