At first I thought Ren’s semblance was invisibility, and that still might be part of it, but grimm see emotions, as we know from volume two. So the loss of colour from Ren’s semblance being activated might not only represent invisibility, but also a lack of emotion. Notice how Nora and Ren both suddenly calm down when it’s activated, and how in RWBY losing colour is typically symbolic of losing emotions and humanity. In the WoR before Kuroyuri, it’s mentioned that many people thought eliminating the arts and their culture, to get rid of emotions, would keep the grimm away. The reason it didn’t work was because their emotions stayed. Ren’s semblance gets rid of his emotions entirely, which is why the grimm can’t find him and Nora: the emotions are what they actually track.
He might’ve realized how it worked, which might’ve played a part in how quiet he is nowadays. It could be part of his strategy, to be less visible to grimm by staying calm.
Also, it would be kind of cool if invisibility to humans was thrown in there too, because he’s also “basically a ninja.”