Theoretically there's two goals for profiles: First, signal strongly what I want to do. Second, show up in searches for things I'm OK with doing. When it comes to an interest I don't care about, I can't achieve both, because either I compromise the signal, or I'll be less searchable. (Someone searches "find profiles into sex and travel"? Sure, whatever, I'll travel, I just don't care enough to have it on my list.)
I want our Yes and Will Try lists to have a Not Important area. I want to be able to add interests there that are searchable, but those should be hidden by default. There should be a link to show those Not Important interests, like: "29 more interests are in this list which the author considers not important enough to show. Click to see them."
I'm not suggesting the same for Mandatory, Core and No because they're always important. Mandatory and Core are what you're all about, while No is what you're absolutely not about. Maybe it'd be applicable for No? I'm just not sure of a scenario in which it would be.
Safe to say search should be a bit smart and try to find people who don't have all the things you're searching for in Not Important. (But then, the current search will also happily supply people who have all the things you list in Will Try and none in Core, so it probably could be a bit smarter anyway.)
Previous feedback about these unimportant interests has been: ability to indicate interests that I don't care about, dismiss a trait/interest, and removing the 100% completion pressure. All of those focused on just not having to add the thing. A reasonable objection has been: "but I still want to know how you feel about that thing", and none of those help you be searchable.