I’m going by dictionary definitions, not what a certain biased organization says.

Would it be biased if they were saying what person 1 wanted to hear?

I wouldn’t deny both of the organizations you mention there are biased. But the dictionary isn’t.

That person doesn’t understand how the dictionary works.

Suppose you are right and the ADL is biased and controlled “by Zionism” (which sounds a bit like a conspiracy theory).

See the response to point 1

What does that make the Snopes organization?

Community sourced fact checkers.

What does that make the literal 50% of America who doesn’t disagree with the ADL?

Idiots. ADL is a good idea implemented and run horribly to the point it doesn’t do what’s on the label.

What does that make the people who call it a double standard that so many people are willing to support murder of one kind but not another

Racists.

or that intentions matter sometimes but not all the time?

Person 1 is incapable of seeing the world in anything but absolutes and shouldn’t be in any position of authority, including over a dog.