Wys - I think you're very wise to think about where your personal line is & then implement it. If your particular style is not compatible with what is being requested then it is surely reasonable to decline. Otherwise you risk diluting the thing that you want to be.
You have made the choices of what you want to play according to a coherent whole, and you shouldn't feel obliged to skew that by playing something that doesn't fit. It sounds as though your repertoire hangs together in a particular context and why should you compromise the hard work you've put in to build that?
For myself, I play and sing whatever I like and I only do it informally. I'm thinking a lot about repertoire at the moment as I think I've fallen into a predictability trap. If I were to play more formally then I think I would be looking for balance and coherence in repertoire & would not be keen to compromise that.
I really hate singing something I dislike, and avoid unless there's a really good reason (eg someone dearly wants to sing it & just needs a helping hand). I think that if I don't have some sort of conviction about the song then I won't sing it from the heart anyway & that always gives me an attack of the drear (and it shows).
The things I most definitely absolutely hate to sing & at which my line would be strongest are 'middle of the road' sort of songs. Though a lot depends on where I last heard the song & the associations it has. Almost anything can be made 'middle of the road' if you try hard enough (or not, if you see what I mean).

Kris