I literally just went to a well known department store in my city and in order to get an advertised discount, I was asked to become a member. This required a SS

I literally just went to a well known department store in my city and in order to get an advertised discount, I was asked to become a member. This required a SSN rather than just email. I don’t trust them with this info and with the SSN alone you can call the bank and identify yourself, the police, and the tax authorities. You can even identify yourself over the phone to healthcare authorites