They don't always get it right - even Faramir & Co were baffled by hobbits and Gollum ....
Remember that most of the ME communities were fairly insular - any stranger probably looked "foreign", styles of dress and speech are giveaways as well as physical appearance.
Also the (for want of a better term) inbreeding probably gave the groups a more distinctive appearance. The rangers were thought suspicious by the men of Bree and they were probably quite distictive by their great height. Similarly in the South there were distinctive groups. Blond Rohirrim and dark gondorians for a start....
I think the elves were probably fairly distinctive but then beautiful people do tend to get noticed!!!
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“But Finrod walks with Finarfin his father beneath the trees in Eldamar.”
Christopher Tolkien, Requiescat in pace
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