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 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.