Other characters having pets but gumball being the kid who has one as a brother isn't breaking continuity....Cool, cool.
Banana Joe and Mrs. G. Lato are bananas and icecream respectively, yet there are episodes where characters are eating both. The entire show is a continuity defect, and that's just the first cartoon that came to mind because I can hear it in the living room. Sure I can' get my daughter to dissect Steven Universe in such a patently absurd way as the OP has RRs since I refuse to watch it.
My point being, the premise of this thread isn't even slightly true.....Since OP couldn't do it and you seem invested, maybe you would like to telly me which modern cartoons follow this solid continuity aesthetic.