Which forums don't you want to see?
Here's an example for me: I only play Civ II, so I have the rest of the Civ forums collapsed. I never get email notifications from them, and of Civ II, only if there's a specific thread I'm watching or have replied to. It's easy to ignore the "latest posts" because I honestly don't notice them. I had to shrink the image on my screen a couple of times to fit this all in and that stuff on the right hand side is usually below everything for me (I'm vision-impaired so things are usually magnified for me).
If you mean you access this site via the Home Page, there's an easier way if it's just the forums you want. You can access by the main Forums page, and it's there that you can collapse everything you're not interested in.
This is what I mean. I've taken a screenshot of what the main forum index looks like to me (well, part of it; it's very large):
First off, I'm using the Dark Theme, so it might not look like the theme you're using. You can see that I can't see anything in the Civ III-VI forums because I've collapsed them (check the oval icons on the right and you can see that I've only enabled the ones for Site Feedback and Civilization II). I can see the Civ II forums, because my favorite Civ game is Test of Time.
There are other areas of this index you can collapse as well. I keep Site Feedback visible, and then nothing else until I get down to the Colosseum, where the Off-Topic, History, Arts & Entertainment, Science, etc. and Archives are. I keep those visible. The rest are collapsed, which saves an
immense amount of time in navigating and deciding what I want to read and where I want to post. And note that even though the latest posts that come up for me might be in a subforum I can't see, I can just ignore that.