An Australian columnist has questioned whether Kiwi Raelene Castle is up to the job of running Aussie rugby.

Writing in the Sydney Morning Herald, Andrew Webster says Castle had not shown leadership over the Israel Folau crisis.

''When Raelene Castle walked into Rugby Australia's shiny new building as its shiny new chief executive in mid-January, more than a few eyebrows were cocked in disbelief at NRL headquarters on the other side of the Moore Park carpark.

''Castle talked a big game in her five years as Bulldogs chief executive. In chief executive meetings, according to those in attendance, she and Souths counterpart John Lee would offer grand theories on how the game should be run but provide little substance.''

Webster said one club boss recounted with a chuckle that: "They were like the two old blokes out of The Muppets who always thought they had a better idea how things should be done than the rest of us."

''Inexplicably, nobody from Rugby Australia spoke to the NRL or the Bulldogs about whether they thought she was up to it. Not NRL chief executive Todd Greenberg. Not Bulldogs chairman Ray Dib. None of them.''

He said when the Folau comments on gays going to hell came out Rugby Australia had dithered about how to respond. ''Castle and NSW Rugby Union boss Andrew Hore finally meet with Folau and his manager, Isaac Moses. Nothing really comes of it, except a Castle doorstop media conference about 'having a conversation' with Folau and that more 'conversations' will be had.

''After meeting with Israel Folau following his controversial comment on social media, the head of Australian rugby union says the player understood he should have been more positive.''

Taylor said this showed that Rugby Australia and Castle need Folau more than he needs them. ''It shows the tail is wagging the dog.

''Castle would've won far more supporters if she called Folau into her office on day one, calmly told him to delete the post, reminded him he's the highest-paid player in the game and that young kids out there hang off every one of his words and if he doesn't like any of that he can go and play another code, or rugby, in another part of the world.

''The game is supposed to be bigger than one person. This week, Castle has shown it isn't.

''When she took on the job, she was concerned about how she would be accepted as a New Zealand woman with a background in rugby league. She was mindful of the game's private school, North Shore clique.

''There was one way to silence the doubters: by making some tough calls and showing some leadership. She's done neither.''