Many followers even likened the Sussexes’ awkward timing to when they announced their first pregnancy with son Archie during Eugenie's wedding in October 2018.
“They had to announce it when Eugenie just gave birth. It looks like something against her. They did the same at their wedding,” one fan wrote on Twitter.
Meanwhile, another added: "Feel so bad for Eugenie: Meghan Markle and Harry overshadow her again with royal baby news.”
A third added: “True to form, the Sussex's try to upstage the birth of Princess Eugenie's first child.”
But despite the social media backlash, royal commentators have since suggested that Princess Eugenie may actually have welcomed the Sussexes’ surprise news.
Speaking on the latest episode of the Royally Obsessed podcast, Roberta Fiorito and Rachel Bowie weighed in on the double up baby news.
“If Eugenie really was upset about that timing of Archie, I don’t think the Sussexes would try to steal her thunder again – I think everyone is cool with it,” Roberta said.
Rachel added: “We’re all still waiting for the name of Eugenie’s baby and I’m so excited and I cannot wait to find out, but … it feels like if you are Eugenie it does kind of suck.”
She continued: “I don’t blame the Sussexes at all… but I do feel like it takes the pressure off Princess Eugenie which maybe she is also thankful for.
"Everyone so focussed on that and now she can just enjoy this time with her baby – not that she’s under the same spotlight (as Meghan) but I do think there is a perk there.”
Roberta then went on to suggest that, unlike other royals, Princess Eugenie has seemingly tried to keep the details of her first baby’s birth more private.
"When people say Meghan and Harry have been stealing her thunder they assume that she wants all of this media attention,” she told listeners.
"Her husband, Jack Brooksbank picked her up in the car and they really rushed her into the car.
"There was no talking to the press or waiting for anything, so I do think they wanted to remain under the radar," she added.