Why we consider identical particles like identical composite bosons for BEC. Why we do not consider non identical particles of differnt masses etc?
The irreducible representations of the Poincaré group are labelled by mass $m$ and the spin $s$.
So as soon you have particles that have different mass, they are intrinsically different and obey their own Bose/Fermi/... statistical distribution.
I assume here that you do not mean idential to be a synonym of indistinguishable. If yes, please clarify.