Is that her?

or

Is that she?

The correct word is "she."

It's a predicate nominative following the linking verb, "is." Since it means the same as the subject, the word must be the subject pronoun.

That is she.
Is that she?

I thought it was natural to use "her", but I guess it is a common mistake.

you are correct in that it is indeed common, though grammatically incorrect, usage.

Just as are

It's me.
Me too. (usually)

The correct answer is: "Is that her?"

To understand why "her" is correct in this sentence, let's break it down and analyze the grammar.

When "is" is used as a linking verb, it requires a subject complement to complete the sentence. In this case, "that" is the subject complement.

The pronouns "her" and "she" have different functions in the sentence. "Her" is an object pronoun, while "she" is a subject pronoun.

In the sentence "Is that her?", "her" is used as an object pronoun to refer back to the person being talked about. The pronoun "that" is the subject of the sentence, and "her" is used to describe or identify "that."

On the other hand, if you were to use "she" instead of "her" in the sentence, it wouldn't fit grammatically. The correct form would be to use the subject pronoun "she" in a different sentence structure. For example, you could say "Is she the one?" or "Is she the person we are looking for?"

To determine whether to use "her" or "she," it's helpful to identify the role of the pronoun in the sentence – whether it's functioning as an object or a subject.