I've never tried completing the spirit temple before the shadow temple but I think the real indication that all temples are completed is when Raaru tells Link to go to the temple of time. Anyway the Spirit temple is supposed to be the last temple you complete, not the shadow temple. I guess you could beat the spirit temple before the shadow temple but either way you have to get the hover boots from the shadow temple before going into the spirit temple. The only temples I know you can definitely do in a swapped order is the fire and water temples. You can complete the water temple before the fire temple because you never need the hammer in the water temple (although it can be used as an easier way to beat shadow link if you don't have the biggron sword).
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