The apology has already attracted more than 78 comments.
Many said the sign was not offensive but merely a light-hearted joke, but others said it was not only offensive to vegans but a homophobic slur.
Vegan Trudi Uttinger said she didn't find the sign offensive and people should be able to laugh at themselves.
But Oliver Rabbett said Pierside should also be apologising for the "queer slur" in the term "pansy".
Numerous people said they would be boycotting Pierside from now on, including Charlotte Drene who said she appreciated the apology but would not be going to Pierside.
"Not keen to spend money somewhere that finds humour in further marginalising minority groups," she said.
A comment from Evelyn Sparks, attracting at least 30 likes, questioned why the sign was put out in the first place.
"I'm pretty sure you put it out there with the sole purpose of causing offense. Otherwise what was the purpose? Like it wasn't even funny or clever in any way."
But there were also comments hitting back at vegans.
"Vegans are offended by everything anyway. You can usually spot them a mile away even before they complain about having eggs in quiche," Morgan Waaka wrote.
The owner of Pierside Cafe and Bar said the sign was a mistake and not meant to cause any offence.
The sign is changed weekly and uses slogans found online, which is where the quote came from.
