There've always been a number of "honorary Amazons", but they usually don't have power. They're often refugees or divine offspring adopted as a sister by the Amazons. They're fully accepted within Amazon society; the best examples are probably Paula von Gunther and Cassie Sandsmark. Currently, there's a character called Maggie.
Oddyssey of the Amazons explained that some Amazons were originally women from Men's World with superpowers, but I've still not finished that series so I'm not sure how that works.