I believe the subreddit chose the mod that would present on Fox news. So I do not think that it was Fox News that did the spotlighting.
Perhaps a nitpick or a misunderstanding, but subreddits don't choose mods. Mods choose mods. The initial mod is just the mod that started it.
If I remember correctly the popular sentiment on r/antiwork re: the mod's appearance on Fox was more along the lines of oh god why but I'm not certain.
antiwork has also largely just embraced the fact that it is a subreddit to bitch about work problems and awful bosses.
You are factually incorrect, in fact the subreddit told her not to do the interview. This has been well documented. It's not very helpful to post your unsubstantiated beliefs when it is very easy to look up the facts.
Do you have evidence of this?
Go look it up. It was all over reddit when it happened. The sub said don't do it and she did it anyway.
Could you elaborate on what effect that is?
Undermining the credibility of /r/antiwork and the labor rights/work reform movement in general.