I think reaction videos are well within Fair Use. By submitting a video to a public platform, you're placing it into the public domain, which allows it to be subjected to commentary, criticism, and parody.
Now, if your video is just 'Oooh' 'woah' 'haha' 'that's cool', then that shouldn't be under Fair Use, because the public doesn't reap any benefit from it. (Ex. Reacting to Try Not to Laugh challenges. Even PewDiePie got a Laugh, You Lose challenge copyright claimed.)
But, if you're essentially 'reviewing' the video by disputing claims, stating your opinion on it, etc. then that should qualify as Fair Use, and as such, you have a legitimate argument to dispute any copyright claims that come your way. Look at channels like h3h3, for example. They react to videos and are still monetized.
However, a lot of YouTubers will claim videos that criticize them, which I don't agree with, because that is essentially censorship.
As a smaller channel, though, take this advice to heart: Don't react to a channel that has a network. Because Fullscreen, for example, can be a massive pain in the a**.