It would be interesting to know how many people make tightly focused characters that want a character-level mandatory interest. I can't see using that, personally. Or only per RP, not at a character level. I mean even if someone is really into pregnancy, they aren't necessarily interested in having every single RP being about conceiving. Maybe a small percentage will be. And as it has been mentioned, it would only be a few interests at most. Again, the concept of a mandatory interest is best expressed at the RP level, IMO.
However, I don't agree with your characterization of Litphoria vs. FList at all. To the degree that Maybe is not the same as Will Try, then BOTH sites are less than fully defined, because you would need both Will Try and Maybe to remove ambiguities and fully cover the range of possibilities. If anything FList Maybe encompasses Will Try, whereas a person's "Maybes" are uncategorized on Litphoria. Or else, Will Try is really a tepid Yes. But again, "Maybes" are still not encompassed on Litphoria.
And most importantly, FList Favorites are the same as the Core concept being discussed. The fact that Litphoria just piles everything into Yes means that Litphoria is actually more ambiguous than FList. Maybe I'm doing it wrong, but at least 75-85% of my attention is paid to the Favorites column. If something important isn't there/doesn't match up, I look in the Yes column for it. If it's there, then I consider our interests to be aligned closely enough. But then in an actual RP, I'm back at the Favorites column, mostly, purposely checking for things and incorporating what I can into the RP. The result is a tighter coupling between "Core" Interests of two RPers. (fuming I am losing entire PARAGRAPHS with this recent change on quotes, asterisks, and parenthesis. Rewriting yet again. )
This is why I say it is more ambiguous on Litphoria than it is on FList. I think it's pretty self-evident. Certainly, creating a "Mandatory category does nothing to reduce ambiguity if there's nothing that I feel should go there. And even if I do put two or three things there, FList still comes out ahead because the "Core" interests are that important of a category for better aligning the most important Interests of RPers.
My preference: Since "Mandatory" should only have a few items in it, make it an horizontally-aligned section above the other Interest columns, and optionally, make it not render if it is empty. When the screen is narrow, all Interest sections render in one vertical stack, so it looks the same as it does now when the window is narrow. With the Core Interests, either add a new column, or else permit Yes Interest to be flagged as Core (essentially creating a Core column as far as seaching/comparing is concerned), with these Core Interests sorted to the top and highlighted in some fashion. (Could do something similar with a Maybe flag in the Will Try column, that sorts those to the bottom.)