Let's be clear, this is a known phenomenon. Foxnews provides an alternate reality, unlike real news, making it exclusionary. and the reality it purports is extreme. It's not just this person's family that has been severely disrupted by Foxnews fixation. It's many.
I dunno, I think the problem is not Fox News but rather the reactions of the family - either those who were watching it or those who were upset at them for watching it. In some cases it's the beginning of a Q-anon pipeline and the Fox news viewer becomes hostile and alienates themselves from the family. In other cases they don't do much other than watch it and repeat it's talking points, but the other half of the family has been equally initiated into blue anon and disowns them for their Fox viewing habits. In all cases, it's not Fox that's the proximate cause, but rather a broken family dynamic that was exposed or exacerbated by the introduction of infotainment.
Many families are able to function with differing political viewpoints inside the family. It's not the red team or the blue team that's the problem. It's people who get so wrapped up in their identity as a member of one or the other that they start to see anyone else as the enemy, family included.