So either they care about the safety of women and children, or they want to have some brown skinned and "weird" people to heave their hate on. I know which possibility I think is most likely...

I recommend this short piece, "The Missing Mood"[0]. It describes the concept that the motive and behavior of someone as it relates to a proposed set of actions is important. e.g. Someone proposing war might be correct, but one hopes a war hawk laments the need to go to war, vs. celebrating it and being bloodthirsty.

Fox News ideology may at times declare opinions that, in complete isolation, might seem reasonable. "Border control", "safe streets", "responsible government" etc. But they approach it from a place of exaggeration and lies, and an outright visceral anger and hatred toward migrants, trans people, etc. They ignore other activities that might be troublesome. Such as ignoring GOP sex offenses, GOP bribery in the oval office, unconstitutional actions by their executive, or needless wars that cost half a trillion dollars and weaken the US' national security.

So I agree with your parent comment, that Fox News and many of its viewers pick and choose what to say they're angry about, either out of intellectual dishonesty or, in the case of the viewer, outright ignorance or deeper thought about the whole picture of the government and society right now.

[0] https://www.econlib.org/archives/2016/01/the_invisible_t.htm...