The heated argument came hours after the release of the couples highly-anticipated sit-down with Oprah Winfrey.
In the 90-minute interview, Meghan said a low point was when Harry was asked by an unnamed family member “how dark” their son Archie’s skin might be.
“In those months when I was pregnant, all around this same time so we have in tandem the conversation of he won’t be given security, he’s not going to be given a title, and also concerns and conversations about how dark his skin might be when he was born,” she said.
Meghan said the remarks were made to Harry and he relayed them to her.
When asked who had made the comments, Harry also refused to give further details, saying: “That conversation, I am never going to share,” adding, “At the time it was awkward, I was a bit shocked.”
Discussing the interview this morning, Morgan said: “What about the behaviour of Harry and Meghan who are spray-gunning his family on global television as Philip lies in hospital.
“I think it’s piling hurt on the Queen who is already suffering greatly from her husband’s illness.”
In response to his argument, Dr Mos-Shogbamimu, an author and activist, said: “I wish to God one day you will even surprise me, you constantly use your platform as a wealthy, white privilege man with powered influence to put out bigoted, sexist, misogynist, racist attacks on Meghan.
As Dr Mos-Shogbamimu was making her point, Morgan interrupted and said: “What a load of race-baiting nonsense..We have done more on racial issues on this show than any other show.”
During the back and forth, Dr Mos-Shogbamimu, who frequently speaks on GMB on issues affecting Black Asian and minority ethnic communities, went on to say: “You want to deny the Royal Family has any racist undertones or actions against the first biracial simply because you’re in love with the Queen.
“You can love the Queen but you should be able to call out actions done by the royal family when they’ve got it wrong.”
In which Morgan responded saying: “I’m not going to let you trash the queen. I’m not going to let you do it.”
Trisha Goddard, a TV personality and former conflict resolution expert, also appeared on the show shortly after the debate.
Morgan questioned whether the conversation on Archie’s skin colour should be considered “automatically racist” to which Goddard replied: “Why is everybody else such an expert about racism against black people.
“I’m sorry, Piers – you don’t get to call out what is and isn’t racism against black people. I’ll leave you to call out all the other stuff you want, but leave the racism stuff to us?”
But the presenter responded by saying that Meghan’s claim was “a very serious allegation” and an “incendiary charge” against the royal family.