Well, to begin, there are no cats and dogs left, only robodogs and such.
I believe that the apes were a special case, and any other modified species would be seen as a mutant, and therefore be kicked out of the city to live in the Cursed Earth, a radioactive wasteland full of mutants.
However, there are plenty of aliens in Mega-City One, and there is a lot of resentment against them by the overcrowded humans.
I guess the most important thing to remember is that pretty much anything can happen in Mega-City One. I remember a story around Christmas where there were some farmers in the Cursed Earth who had "bred" modified turkeys, so they the turkeys were self cooking. They were intelligent enough that they would pluck themselves, turn on the oven, get everything ready and then climb into a pan in the oven to cook. Of course, one turkey got smart, and tried escaping... and with a few friends... he's probably still out there somewhere.