Poppies are worn each year to mark Remembrance events and commemorate those who died in the first and second world wars and other conflicts.
Schillemore said a couple of women, after overhearing the exchange, had said they would not support a business that refused customers wearing poppies.
“The door staff at the time only had to say ‘Fellas, not today’, and that could have been it,” he said.
“It was at the point that he said that the poppies was the reason and that’s what upset us all.”
A Wetherspoons spokesperson said there was “no ban on poppies” in the company’s pubs.
“Wetherspoon has been a long-standing supporter of the Royal British Legion Poppy Appeal, with poppies for sale in our pubs, including the Star,” they said.
It said security measures during the demonstration on Sunday meant “some members of the public, including some wearing poppies, did not gain entry to the pub”.
The spokesperson continued that it had closed to all customers at 17:00 BST after advice from the police, and remained closed on Monday.
“We apologise to any regular customers who have been inconvenienced by today’s events and look to forward to welcoming everyone back tomorrow,” they added.