Buddhist influence on the West is way older. It goes back to Hellenistic era, https://en.wikipedia.org/wiki/Greco-Buddhist_art
Not unlikely Christianity was influenced by Buddhism, https://en.wikipedia.org/wiki/Buddhism_and_Christianity.
And certain groups, especially a Gnostic creed Catharism, has a lot of similarities.
Reminds me of the movie Man from Earth (don't watch the sequel). The precepts of both Christ and the Buddha are quite striking in their similarities, but perhaps both are a manifestation of an even deeper principle, of what it means to be a good person.