Xenforo is extremely customizable so I'd expect that it is possible to remove reactions from appearing in the newsfeed or even just for a specific page. However, they are likely deeply imbedded in the forum software and changing one thing results in unexpected changes elsewhere.
I have played with Xenforo a little trying to create a small forum that I never actually published. I am just not into programming and don't want to spend the time and effort to learn. If its not in the management panel than I don't know how to fix it except that it can be done. There are businesses who will customize Xenforo and charge a fairly high price. Then, when the forum software has a major change, it might break the customization.
The news feed of user activities includes all those reactions (likes). They feed to the Xenforo system by default, a expert could filter them out of the news feed. If you know what to do, it might be easy, or it might involve a huge amount of work. I'd suggest asking CR guy to consider removing the reactions from the latest activity page. It may be something for his to do list or it may be impractical.
Welcome to the third in our "Have you seen...?" series for XF 2.1. We've had a phenomenal, er, reaction, to what we've shown so far. In case you haven't seen our previous two entries, you can check them out here. As ever, to ensure you're kept up to date, we strongly recommend giving that...
xenforo.com
I think that you might just consider that the latest activity page is just that, a log of user activity in the public areas.
I saved a link to "New Posts" and use that to open the CR forum so they are the first thing I see.