Mama,
the first amendment does specifically cover freedom of press.
and a slight correction in order: when she made those remarks, she wasn’t on her employer’s time. It was a private conversation b/w two private citizens at the end of an event at white house. rabbi Nesenoff was asking random people about their views on Israel and thats when he approached Thomas to seek her views.
I find her comments distasteful but the bigger issue here is not the freedom of speech/press, rather the equal treatment of bigotry towards other factions of the society. would she have been treated with same equal ferocity had she made such comments against, say Asian immigrants in the US? would they’ve asked for her head? I highly doubt it. this is where the sense of injustice pops up. you can say pretty much any thing you want against a certain group of people/religion/belief and you’re protected by the freedom of speech right but it suddenly becomes a cardinal sin to say a word against your favorite ones.