Is it - or could it be - possible to mute threads so you don’t see them in the new or recent posts feeds?
Not yet. This is definitely a feature I want to add - once I've got the site upgraded to the new forum software, I will be looking to add this functionality. It's very important for one of my other sites too - so it's high on my list of priorities. My vision is to be able to mute threads, forums, media categories and even members (although you can already do that using the ignore function - but I plan for muting to work slightly differently).