Though the couple is reportedly expected to release photos from Archie's big day, the actual event won't be open to the public, leading to some backlash from Brits.
"There was some criticism, some debate when the Sussexes said that they wanted to keep their birth plans a bit more private," Murphy told ABC News. "We're seeing the same thing is happening now with their christening plans."
About 25 people are expected in attendance at the christening, including Prince Charles, Camilla Parker-Bowles, Prince William, Kate Middleton and Duchess Meghan's mother Doria Ragland.
The queen is said to have a prior engagement and will be unable to attend.
Duchess Meghan and Prince Harry have kept Archie's privacy paramount, even nixing giving the baby a royal title in hopes of allowing him a relatively normal life.
Duchess Meghan's estranged half-brother, Thomas, previously said he and the rest of her estranged paternal family would like invitations to Archie's christening, but that seems less likely now than ever.
Prince Harry and Duchess Meghan will visit Africa this fall with Archie in tow.