Entropy is related to the number of ways a certain situation can be realized. The more microscopic ways there are to create the same macroscopic situation, the higher the entropy of this macroscopic situation.
https://en.wikipedia.org/wiki/Entropy
I believe, you forget that though atoms are not unique, they are treated as unique individuals in this context.
Let's say, we have a crystal consisting of 4 metal-atoms. There are 4!=24 ways to build that crystal. If we have a crystal of 2 Na and 2 Cl-atoms, there are 2!*2!=4 ways to build that crystal.
Let's say we compare an ice-crystal and a water-droplet. The ice-crystal is an ice-crystal only if the water-molecules are at the right locations. The water-droplet is still a water-droplet if the water-molecules are slgihtly out of position.
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There are more ways to make a water-droplet than to make an ice-crystal.
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Liquid water has more entropy than ice.
Let's say we have a non-living matter and living matter. The non-living matter stays non-living matter if a few atoms are slightly out of place. The living matter dies if too many atoms are out of place.
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There are less ways to make living matter than there are to make non-living matter.
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Living matter has less entropy than non-living matter.
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