Ok but I don't know what you mean by spreadable butter Vs block butter so I can't give you an opinion.
By "spreadable butter" do you mean stuff you get in plastic tubs like clover or I can't believe it's not butter or something?
Because I've never referred to that as butter (because it's not)
If that is what you mean, then it is supposed to be in the fridge.
If you mean actual butter, a spreadable type made a certain way that I haven't heard of or aren't aware of (very likely as I often hear on Mumsnet everyone seems aware of except me) then yeah, it should stay out of the fridge, because it's butter.
But either way, regardless of what does or doesn't go in the fridge, you are right and she is wrong by default, because she is interfering in stuff that isn't her business and should stop being an interfering old busybody.
So yeah, I voted YANBU but would be grateful for clarification on the butter naming situation