Meghan Markle and Prince Harry are perceived to act in a way that sets them apart from the Duke and Duchess of Edinburgh and Princess Anne.
The claim has been shared by the royal expert Richard Fitzwilliams.
The California-based royals are set for another "faux royal tour" following their successful visit to Nigeria in May.
Richard Fitzwilliams, a royal author, spoke to Svar Nanan-Sen, GB News's Royal Editor, and Cameron Walker, the Royal Correspondent, on this week's episode of The Royal Record podcast.
Svar asked Fitzwilliams if Meghan, 43, and Harry, 39, will no longer issue public attacks on the Royal Family.
The commentator replied: "Well, I rather fear there's more to come. I would like to think that given the circumstances, and given King Charles and the Princess of Wales's illnesses, that they would stop attacks.
"But we saw Harry in the ITV documentary talking about alleged tabloid excess. He was discussing the rift with his family and their very different attitudes had made the situation worse, indeed it had been one of the causes of it. So it's impossible to say."
In a clip from the documentary, journalist Rebecca Barry asked the royal: "To what extent do you think your determination to fight the tabloids destroyed your relationship with your family?"
Prince Harry replied: "It is certainly a central piece to it."
He added: "I think that everything that has played out has shown people what the truth of the matter is, for me the mission continues. I think as you say, it has caused part of a rift."
Fitzwilliams continued: "The sort of attacks that we saw in Oprah and with their Netflix series documentary were bad and the interviews were pretty brutal. Decency would forbid that they repeated those.
"Allegations have come out that Meghan could write a memoir. Harry had 400 pages in Spare, so it's possible some attacks might emerge. They know every single thing.
"This is one of the reasons that Colombia is important because it does show that they have a very high international profile."
Harry and Meghan are set to visit Colombia this summer on an unofficial royal tour, at the invitation of Vice President Francia Marquez.
Fitzwilliams remarked: "The fact the Royal Family is on holiday means they wouldn't be conducting overseas tours at the moment.
"It is very, very difficult for both the King and Queen and also for the Prince and Princess of Wales to do that.
"It does tend to indicate with royals such the Duke and Duchess of Edinburgh and Princess Anne that [the Sussexes] are on a different level.
Harry and Meghan know that they are being followed by huge media, international media, and that will, I suspect, give them a sort of an edge.
"I would hope that they would not criticise the Royal Family. Just consider for a minute that they decided to say something nice about the institution or the Commonwealth.
"Imagine the Sussexes making some form of gesture and saying something that was favourable. We haven't seen any of that and it's been a long time since they've done that."
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