Your priest is partly correct and partly incorrect.
There is nothing wrong with offering a meat option for your non-Catholic and non-Christian guests because they are not bound to observe the Lenten abstinence from meat. Your Catholic guests, though, are
bound to observe the abstinence.
The exceptions to that rule are when the Lenten Friday falls on a solemnity (the Solemnity of St. Joseph on March 19 being the solemnity that falls during Lent) or unless a dispensation is given for the Catholics to eat meat. Ordinarily, such dispensations are given by the bishop and during Lent is sometimes granted by a bishop for St. Patrick's Day. Since your wedding will fall on St. Patrick's Day, at this point neither exception applies to your circumstances.
If you feel it necessary to offer a meat option for your guests, you're free to do so. I recommend though that you inform your Catholic guests of their obligation to observe the Lenten Friday abstinence. You can do this by placing a note on the invitation to the rehearsal dinner or you can informally "spread the word." Or, if you are uncomfortable with either of those options, you could limit the choices to fish and vegetarian on the grounds that fish is a meat that all of your guests will be able to eat that day.
Why meat but not fish?