was imagining Mary's real interaction with Maria and Julia as being very different from the way she describes it to Fanny.

I'm not sure if I'm right here, but I was imagining she was probably opportunistically playing Maria's and Julia's best friend and putting Fanny down

I dont think that that is the case. I dont think that the Bertram girls would notice her "putting Fanny down".. Neither of htem has any great interest in their cousin, and would probalby be jsut bored by any reference to her..
of course Mary is polite to Maria, and friendly but I think that she does not really like her much. I think that her present liking for Fanny is sincere, though short lived.. She sees Fanny as a genuine person, much more so than Maria or Julia and would like to be her friend.. But her primary loyalty is to herself.. If circumstances parted her from F for a while and Henry lost interest in her, Mary woudl soon forget about her.