The woman, thought to be in her 30s, delayed flight MT105 from Dalaman, Turkey to London by 70 minutes on Friday morning and launched into a racist rant.
She told staff they were “disgusting” for making her fly with the trio and that it “shouldn’t be allowed”.
The plane eventually took off at 2.25am local time after the woman was escorted off the plane by police – to jeers from fellow passengers.
Shamea Oldham, 18, from London told Mirror Online: “She was stood at the front of the plane screaming abuse. She kept saying she didn’t want to fly with them and refused to let the plane take off with them on board.
“She said the other passengers were disturbed to want to fly with them.
“What she was saying was appalling. She was screaming saying they were a ‘threat’”.
Dad-of-three Mario Van Poppel, 40, was returning from a family holiday with his pregnant wife, 11-year-old son and twin girls aged 4.
He tweeted: “A passenger on our Thomas Cook flight #MT105 from Dalaman to Gatwick refuses to board the plane because three bearded men in white prayer robes are on board.
Mario added: “It went on longer and longer until another passenger asked a flight attendant what was happening. She said the woman was refusing to board the plane.
“They were trying to talk her around but she wasn’t having it. Eventually she came back to take her hand luggage off the plane.
“What she was saying was appalling. She was screaming saying they were a ‘threat’”
Eyewitness Shamea Oldham
“She was swearing and was very aggressive. She used the word terrorist.”
A Thomas Cook spokesman told Daily Star Online: “Two passengers on flight MT105 from Dalaman to Manchester were removed from the aircraft by police following offensive behaviour on board.
“The safety of our customers and crew is always our first priority and we do not accept this kind of behaviour on our aircraft.
“We are sorry to our customers for the delay this caused to their flight.”