"Wonderful for [the Australian Republican Movement], however, as it highlighted ludicrousness of placing primacy on family that doesn't return favour!"
Peter van Onselen, a political commentator, added: "It was great watching our royal family cheering on our opponents at the rugby World Cup today. Yep, it's ridiculous..."
Prior to Australia's victory over England, Fitzsimons said he had offered Prince William a Wallabies jersey after the royal, who is vice patron of the Welsh Rugby Union, wore a Welsh jacket during England's game against Wales.
"Good fellow that he is - and I mean that - he's also marked down as the future king of Australia," Fitzsimons wrote in Fairfax Media.
"You'd expect then, wouldn't you, that as our future king, if he can do that to support the Welsh, he could at least wear the Wallaby jersey at Twickenham?"
Following the game, the social media banter continued as supporters of a republic called on the royal family to support Australia at future games.
Lisa Wilkinson, a prominent broadcaster who happens to be married to Fitzsimons, said in a tweet: "So you all reckon Prince William will wear Welsh jersey when #Wallabies play #Wales. Why? Isn't he as much our future king as theirs??"
The Australians for Constitutional Monarchy responded to Australia's victory with apparent restraint, saying on Facebook: "Congratulations to the Wallabies, as Australia defeats England."
Support for an Australian republic has waned in recent years but the movement has been buoyed in recent weeks by the rise to the prime ministership of Malcolm Turnbull, a former republican movement leader who ousted Tony Abbott, a staunch monarchist.
- Telegraph and NZ Herald staff writers
