***** NOT A TEACHER *****
Hello,Here in the United States of America, people are very careful not to say anything that may hurt another person's
feelings about race, religion, love life, etc.
So some people use the word "persuasion" because they (a) want to be gentle and kind, or (b) they are being sarcastic.
That is, they know that if they ask a direct question ("What is your race?"), that may offend some people. Those two
cops (I am guessing) had been ordered not to ask such a rude question. So they were probably being sarcastic when they
might have said, "Excuse me, sir, what is your ethnic persuasion?" (The "sir" is also often used in a sarcastic manner. They
might like to use some other word, but they know that they would get into big trouble.)
*****
In plain English, if someone asks you what your ethnic persuasion is, he wants to know what your race is.
Some people do not want to mention the words "race" or "ethnic," so they just say, "What is your background?"
*****
As Chicken Sandwich told you, Americans no longer use the word that you used in your post. This stopped in the
1960's. Until then, it was not an offensive term. Whenever you speak or write English, never use it.
James