They're really in a damned-if-you-do, damned-if-you-don't position at this point. On one hand, the News Corp top brass are probably not, and probably never have been, part of the cult themselves. They're too smart for that. (Which really says something about all the public figures that aren't.) But they also have to pander to their target audience, which is still mostly die-hard cultists. They're not the only right-wing media outlet in America. Counting on their audience to be too lazy to stop watching and find somewhere else to get their "news" gives them some wiggle room to question Trump's policies, but it's a tricky balancing act.
And then there's the question of what the implications are if Trump is serious about his plans to become a dictator. How likely he is to succeed, what the fallout will be for his purported allies if he fails, and whether News Corp is actually in a good position to reap any benefits under the United States of Trumpland. Dude's probably going to want a State Media, after all, and as the owners of both the highest-rated news channel in the country and a number of prominent newspapers, just promoting News Corp into that position would be the laziest way to do that. And we all know Trump prefers the lazy option. But it will definitely come with the stipulation that they fire everyone that he remembers not consistently kissing his ass, and that anyone caught questioning him afterwards might get worse than that.
It's funny, actually, when you think about it. All other factors being equal, a news outlet dedicated to bashing Democrats is going to get the best ratings if the Democrats in question are actually in power. But because words have power, if they bash them too effectively, the Democrats won't stay in power. And also also, News Corp isn't just hitching their wagon to the right because it's good for ratings; they're doing it because those are the people whose policies they personally support. Except for the one loudmouth who happens to be the de facto head of the party at the moment.