Think of this way: there's some sort of algorithm that controls what goes on your Facebook feed. There has to be, basically, or else they just have to show you everything. The algorithm takes in sentiment analysis as part of making those decisions, which seems perfectly reasonable. So far, just by building something that interacts with users and affects their emotions, FB has a completely uncontrolled experiment. If they show negative stories vs positive stories, what happens? So far, they just don't know, which seems really bad. Well, to find out the consequences of what they actually do, they have to dial up and down some knobs and see the effects. If they can't try things and find out what happens, how do you expect them to do anything? Just guess? Even worse, if they just guess, they're still experimenting, but now with way less information.
This is completely normal, and every business does it. They have to answer questions about what effect the things they do have, or get stuck not doing anything. A huge part of what businesses do is interact with people, so a huge part of that effect is actually the impact on their customers' emotions. What if we make the colors on this display brighter? What if we play different music in our store? Psychology experiment! You can call it "manipulation" if you want, but you're really just going for cheap connotation points. Almost any editorial decision you could make on any subject with any audience is manipulation. Being systematic about it doesn't make it more so. Do you think you should be asked for consent before being subjected to an A/B test on an ecommerce site? Because you're definitely being manipulated in the relevant sense.
It sounds to me like the objections are not so much that FB ran an experiment so much as it's that they published a paper about it. You could argue that that really is dispositive, but, well, nobody is. And it seems if they're going to do some research, we should actually encourage them to share their results.