Rainbow Devils said in a statement that members were informed "shortly before the game that these jackets would not be worn".
"The reason being that one of the matchday squad had refused to wear the jacket on the grounds of their personally held beliefs," the group said.
"Therefore, to maintain the team ethos and togetherness, none of the players would be wearing them.
"We respect the right of this player to have his own views, whilst also feeling disappointed that he put the rest of the squad into a position where they felt that they couldn't wear their jackets.
"We also worry what kind of negative effect this incident might have on any player at the club who may be struggling with their sexuality."
On Wednesday, the Football Assocation said it was taking no formal action against Crystal Palace or captain Marc Guehi after he wrote a 'Jesus loves you' message on his rainbow armband for the club's win over Ipswich the previous night.
Guehi and the club had been reminded by the FA that religious messaging on kit is banned after the 24-year-old's rainbow armband in Palace's draw against Newcastle United on Saturday had the message 'I love Jesus' written on it.
Ipswich captain Sam Morsy did not wear a rainbow armband again on Tuesday, after his club said he elected not to do so at the weekend because of his "religious beliefs".