Just in case anyone needs a reminder all dungeons and raids in TBC Classic Anniversary are account wide. Once you complete it on a character any other characters on your account will also be attuned.

 Blizzard Entertainment

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Heroic Dungeons
Every player’s first character will be required to become fully attuned (hitting Revered reputation level), but upon doing so for each dungeon, players can then purchase a Bag which contains a Bind-on-Battle.net-Account key to send to alts.

Alts must reach at least the Friendly reputation level to use the key and grant attunement to that character.


Raids
Every player’s first character will be required to become fully attuned for each Raid, but upon doing so, that raid will be unlocked for all characters on the player’s Battle.net account.

Raids will be released in their post-nerf state.

Source