You don't get to pick and choose what Fox News has said in the past. Their position is that climate change is vastly exaggerated and largely a hoax, and depending who you talk to they might have a stronger view.
You don't get to forget what they said in the past and present and choose a totally new position, where the main focus is on hypocrisy. Because if Fox News believes what it has said for the last 20 years, then the actual reasoning is that Taylor Swift is acting hypocritically but it's irrelevant. In other words, if they want to have integrity they would need to undercut their own story.
You personally are free to have a position that purely focuses on hypocrisy if you haven't already made public statements on climate change. But Fox News is stuck with positions it has already endorsed and continues to endorse. I mean we know that Fox News has no credibility but if you thought that they should, then this is something they can't avoid.