In older writing, one would have used the phrase literally, to describe someone's religious or political affiliation: beliefs one could have been "persuaded" to adopt. One might refer to a preacher "of the Methodist persuasion", say.

The modern usage of the idiom came about as a joke - as though someone's sex or ethnic heritage were merely a matter of preference. Over time, the original sense has been forgotten, and the humor has been lost through repetition, so it is now just an odd phrase.

The US TV show "All in the Family" in the early 70s included the character Archie Bunker, who was an outspoken bigot. This might have been the origin of using "the Oriental persuasion" as a joke. My parents thought it was hilarious, and explained the joke to me. Yes, since then, that usage has leaked from being humor to being used in the sense above.