It depends, racial coding (and coding in general) is kinda unavoidable. People are free to interpret your character's traits as they wish and that means there will be repercussions for the things that they project onto them. So it is benificial to be intentional with your coding of your anthro characters as to avoid falling into harmful stereotypes by accident.
On the other hand, if you are just taking a deer and making it talk, the racial coding that audiences assign to that character are not 100% on you. An example is how the meercats in the lion king reflect a lot of experiences associated with jewish communities, and how this has both positive and negative readings but also may be completely unintentional! more on that in this video that I'd totally recommend. (the title is a little inflammitory so bear with me).
Racial/ethnic coding in anthro designs can be used for interesting social commentary (as with maus), but it can also be kinda weird and stilted (as with zootopia). Ultimately anthro art is symbolism, which you can use if you desire but can also be taken from you work either way. Its worth bearing in mind (especially if you plan on doing gorilla/monkey anthros, those can get pretty bad prettty fast: see animal crossing)