The sign is one of the many efforts in that direction, the owner says.
He says the sign is not meant to discourage parents from visiting or make them feel unwelcome. However, disposable nappies are hard to get rid of in a sustainable way and staff have had a number of situations where they found nappies clogging the toilet or even left in the sink or on the floor.
The café only has three staff at any given time and, when the toilet needs unclogging, kitchen service has to come to a halt.
McNelis says that, had the mum asked the staff about it and explained that she needed to change her child's nappy, they would have taken the nappy to the skip bin around the back where they keep non-recyclables.
The mum posted in a local parenting group and, in the space of a couple of hours, the business was flooded with negative reviews from outraged parents.
The woman who runs the parenting group met up with the café owner.
"The lady who originally posted online didn't speak to the staff or anything, just took a photo and posted it," he said.
McNelis says he sat for "a cuppa" with the admin of the local Facebook group and explained what happened.
"I can see how she got the wrong end of the stick, but if she'd spoken to the staff we could have explained," he said.
"It all blew up, people love to be offended."
There were so many negative reviews coming in that Facebook started moderating them and TripAdvisor suspended reviews for the business, to stop the influx.
Barley's big bold waste-free goal
When Matt McNelis and Freya Thomson travelled to Cambodia last year, the heartbreaking scenes they saw were etched in their minds.
"We were really saddened us to see rivers that you can't see because they're covered in plastic. It's a whole beautiful country drowned in plastic waste," he says.
When they decided to open their vegan eatery, McNelis retired from his career as a jockey and decided to set Barley up with the goal of becoming one of the first hospitality businesses in New Zealand to go "zero waste".
That is the goal they have been working towards since the beginning.
"In hospitality that is quite difficult. I talked to all the suppliers that we use and explained what we were going for. If it's non-reusable plastic, it'll be going back on the truck," he said.
Their produce now comes in cardboard boxes and everything is either in re-usable or biodegradable plastic.
The café has different bins for paper, plastic, cans and glasses and every evening Matt goes home and sorts through everything.
"At the moment, we generate very little waste."
Disposable nappies, when a customer asks, still have to go in the bin at the back, as there isn't much more that can be done about them.
Despite the bad publicity and the loss of business, McNelis says his waste-free goal remains intact.
"I might re-word the signs on the doors to explain why our policy is what it is, but the policy is not changing."
He says, for a small café in a small town, the bad reviews were "a kick in the gut".
"It's hard. You're a small business and in two and a half hours we had 30 to 40 bad reviews by people who had never visited us.
"I had one of the 'internet trolls' message me on my private page saying 'I hope you go out of business'," he says.
"In a small business in a town like this, bad reviews do a lot of damage. It would have been less detrimental if you'd smashed our windows."