I agree, but I think that it is part of Fanny's nature.. and one has to remember that she has not had much experience of social life and lively not to be taken too seriously conversation...

(whether she ever becomes more relaxed we dont know but maybe she will later if she's more secure).
She has little to sustain her emotionally.. SHe knows she's a poor relation, that most people at MP hardly notice her or think well of her.. All she has is Edmund and he too is a serious rather heavy young man who does not find it easy to make light hearted conversation and lighten the dullness of MP...But F has grown up under his influence and has also had Mrs NOrris and Sir T dinning it inot her that she must be a good girl and in effect be grateful for all the family have done for her... and that to be ungrateful for the fireless room, the being Lady B's knitting companion etc etc is a terrible thing on her part.
So F sets out to be very "good" IMO and has to deny any part of herself that is less than "good"... She can't be angry with people on her own account so she has to displace it into being angry that they dont come up to her moral standards... and even then she's afraid IMO to feel anger at her cousins for not being "good"....