Learn English – Word for an Original Idea

Consider "I'd rather to not say" and "I'd prefer to not say". In my book they grammatically (even mathematically) equal so we can simply compare the two individual words which are different. Otherwise there's the obvious reason that you've used a more grammatically formal construction which makes "I'd [verb] to not say" more formal than "I'd [verb] not say".

'Prefer' has a Latin root (1) whereas 'rather' and 'sooner' (2) have the same old English root, cognate with many Germanic languages. Often using the Latin-derived words sounds more formal so that's probably why you think it's more formal. Historically Latin was the common language, especially in academic circles, between various European states and so naturally the "more educated" or "more formal" language would use Latin or Latin-derived words rather than old English.

1. Prefer: French and Middle French préférer from Latin praeferō.
2. Rather: Middle English rether from Old English hraþor from Proto-Germanic hraþaz

I like hidebound for this purpose, which in one of its senses means "stubborn; narrow-minded". Of course narrow-minded ("having restricted or rigid views, and being unreceptive to new ideas" or "intolerant, bigoted or prejudiced") is a possibility too, along with reactionary ("opposed to change; urging a return to a previous state" or "very conservative"), small-minded ("Selfish, petty, constrained in thought, limited in scope of consideration" or "Not interested (or capable) of thinking about the big picture"), insular, monomanic, having a one-track mind ("obsessed with something or only able to think of one thing"), or having tunnel vision (focussing "one's attention on one specific item or event, to the exclusion of everything else").