> in the logic of OP, all other dogs who think this is behavior is okay
No. The OP did not talk about approval. They talked about specifically thinking the candidate is racist.
Now, it's possible that Candidate X is not a racist. But if the racists are confused about it, maybe Candidate X needs to be more clear. Because the racists look at Candidate Y and "We hate Candidate Y, because they're opposed to our beliefs". No chance of misunderstandings there.
Now, Candidate X will certainly have other supporters saying "We don't believe Candidate X is a racist", but I look at them sidelong and say "Don't listen to me, listen to the racists".
The dog has no concept of "the bad elements".
A dog isn't a reasoning human being. Using the dog, this way, in the argument is irrelevant and distracting to any of the issues.
I think we can say that EVERY person around Hitler was in fact a bad person regardless of whether they loved dogs.
It may be that people used fallacious reasoning to justify their own support of Hitler (ignoring his other qualities conveniently) for such reasons as "he likes dogs therefore he is a good person".
"I like X because he agrees with me in this narrow way therefore I'll support X doing terrible terrible things but justify it with this narrow reason."
That's a bad person supporting a bad person.
Person A prefers apple over oranges and potatoes over tomatoes.
Person B prefers also potatoes over tomatoes but does not care about apple or oranges.
Original poster now argues that it is okay for Person C to say Person B is an oranges hater, just because Person B prefers potatoes.
Replace Person A/B/C with your favorite groups of adversaries.
As a consequence, when people have the gut feeling that something might be off many trust that feeling over whatever truth is them presented.
Also: >> (Or, as a friend put it about politics, "If the racists think the candidate is a racist, the candidate is probably a racist".)
is just amazingly simple minded. By the same logic all dogs are Nazis just because Hitler's dog (probably) loved him and Hitler was a Nazi after all.