I am not sure if you are saying you have to go back 50 years to find them or you can only find them going back 50 years?
Anthropomorphs have lots of cartoons of actual cats who walk and talk and are sentient. Felix the cat was animated in 1919 before there was even sound movies.
Flash Gordon had lion men starting in 1936, though that is print cartoon and not animation.
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For more modern things you have
Thundercats Roar from 2020 (also Thundercats from 2011 and the 1985 original series).
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In general I think I think it is arguable there are more anthropomorphs than elves and dwarves in cartoons. I would think there are more instances of ninja turtles than dwarves for instance.