Actually, you need the Lens of Truth to get to the Spirit Temple, and you can't get the Lens of Truth without completing the Forest, Water, and Fire Temples..and from the last post, of course you can do the Shadow Temple before the Spirit Temple, that's the way it was intended..you must have wrote it wrong. Next time I play OoT i'm going to try Forest, then Water, then Fire, then Spirit, then Shadow. Seems interesting but I won't be doing OoT again for awhile..
Without glitches you can actually get the Lens of Truth as soon as you complete the Forest Temple because you have to be able to go back in time. Also the Lens isn't absolutely required to beat the game, but it's practically required. You have to know the game really well to beat it without it.
Once I've beaten the adult portion of the game in this order: get the hookshot, beat the ice cavern, complete up to the longshot in the Water Temple (the bow is needed for the last two keys which lead to the boss key), complete the Gerudo Fortress, cross the Haunted Wastland without the lens of truth, enter the Spirit Temple for the Requiem of Spirit, beat the Forest Temple, beat the Spirit Temple, beat the Fire Temple, finish the Water Temple, beat the Shadow Temple, and then beat the Bottom of the Well.