Hi. To me that looks like algae, but I am no expert. We get this kind of buildup in the toilet tank and I have seen it come out of whirlpool jets. I have been told that it is harmless in those situations though I don't know about it being in your drinking water. I found this article that talks about how to clean water dispensers on refrigerators; perhaps your brand is listed or it will give you an idea about how to proceed. Otherwise, your owners manual may have cleaning info. Apparently, these systems are supposed to be cleaned, but I had no idea about it. https://www.waterev.com/how-to-clean-a-refrigerator-water-dispenser/

p.s. I am not a member of this subreddit, so I hope this post is acceptable.