I try not to cut myself off the information, but instead I change the way I process it and interact with:
1. Minimize the time spent discovering the information.
Obvious step here is using RSS so you can read about interesting stuff when you feel like it, not when it appears in your news feed.
Another thing I'm doing is setting up search alerts for topics that interest me, so I can look at them once in a while (e.g. once in two weeks), skim through and bookmark the most promising ones for reading later. I'm using a tool I wrote myself that can search over hackernews, reddit, twitter, github, etc. for topics that interest me and convert to RSS feeds. It's kinda like Google search alerts, but nicer. I haven't documented it properly yet though, but started it here [0].
2. Prioritize reading, don't read immediately
For example, I would only read Reddit once a week, going through the weekly top (and all of new posts for some select subreddits). On the first pass, I only bookmark stuff, I don't read it immediately (unless it's something really exceptional, or it makes sense to comment as soon as possibile). Another benefit is that I can also do it on the go, without spending mental resources on proper reading.
Now and then I would go through the list of saved items, and choose what I want to read next. That way it doesn't feel like I'm missing out on anything, I'm aware of the information and can find it in in case I want to catch up later.
Most apps offer a pretty horrible experience for such workflow (i.e. you can't put priorities/reorder/search), so I've got my own workflow using org-mode to process the information. That way I can also leave comments, or refile it in my knowledge base immediately. I'm describing it in more details here [1]
3. Make it easy to find information
One big thing that reduces my FOMO is knowing that I can instantly find whatever interests me on my filesystem when I need it. I describe my system and setup here [2]. You can also get a glimplse at the public part of my wiki/knowledge base here [3]
[0] https://beepb00p.xyz/axol.html
[1] https://beepb00p.xyz/orger-todos.html#reddit
[2] https://beepb00p.xyz/pkm-search.html#personal_information