I really think that it's poor taste to protest politicians at their personal house. This has been happening in Portland at the Mayor's house and in Seattle at the police chief's home. It's a good way to have people in the middle turn away from you.
Fox News is protesting?
Kind of, but more like activism than protesting. Hannity was engaging in faux journalism, sending his crew outside Biden's home...harassing him for "hiding in his basement bunker" at his "compound" which was part of the conservative talking point at the time. Sending in an overnight camera crew to a residence to slander Biden is part of some slick political operation shtick. Granted, some conservatives really believe Hannity is a journalist, courts might declare he is an entertainer, but I think it's clear he was engaging in the same kind of attention getting as someone outside Tucker Carlson's house with a megaphone asking Carlson why he's a racist. ... except those activists might have a more legitimate point.
It may be up for interpretation somewhat, but here's a link:
https://www.thewrap.com/hannity-has-fox-news-cameras-camped-outside-joe-bidens-house-lawrence-video/