Although I do not practice law in the States of New York or New Jersey, here are my initial impressions.  First, you need to provide more information.  How was your shoplifting charge resolved?  Whether it resulted in a dismissal, nolle, or conviction, for example, will affect whether and where it will show up.  Once you have determined the resolution, you will be able to start to figure out the contexts in which it will show up, if at all.

You need to look into the possibility of an expungement, starting at 2C:52-1. Much depends on the amount alleged to have been shoplifted, for example, if the full retail value of the merchandise is less than $200.00, you are dealing with a disorderly persons offense which may be expunged after five (5) years following the date of conviction. A conviction for 2nd, 3rd or 4th degree shoplifting may be expunged after ten (10) years following the date of conviction. Call me at (732)932-7226 (office) or (732)710-0004 (cell).