In a post on the European Playstation blog, Sony's Fred Dutton confirmed that the multiplayer in The Last of Us Remastered on the PS4 will not be changed from the PS3 version.

To those not in the know, the European version, even outside of Germany, was heavily censored and featured no gore in the multiplayer component. When asked about this for Remastered, Dutton confirmed the news no European wanted to hear.
What about the gore in the multiplayer? The PS3 version for Europe was less violent because of some countries such as Germany, but what about the PS4 version? Details please.

While the single player should remain unchanged, the multiplayer will remain heavily censored. It is quite odd that Sony would make such a move to censor all of Europe when it's really only Germany where the game should be heavily censored. Many European gamers are opting instead to import the game from North America.