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.