What is the logical fallacy that feminists commonly use to vandalize during protests?

Protestant reasoning is usually formulated as follows:

1. Person 1 states that protesting violently about a violent act that was committed against a woman is wrong.
2. Person 2 (who is the feminist who protests) states that violence is the only way the authorities can listen to them.

I suppose that the fallacy you're fishing for is that "Two Wrongs (Don't) Make a Right." But your question is quite loaded.

In any case, moral justifications can get very complicated. The Japanese attacked Pearl Harbor (violent act). US responded by declaring war (violent act). Was that wrong? Don't oversimplify complicated questions.

Let's remove any bias here and get to the heart of the question:

1. Person 1 states that protesting violently about a violent act that was committed is wrong.
2. The protester (person 2) states that violence is the only way the authorities can listen to them.

Person 1 is stating an opinion (unfalsifiable).
Person 2 is also stating an opinion, but one that is falsifiable. Non-violent protests have a history of effectiveness, so person 2's position is easier to argue against.

I see no fallacies.

There is no fallacy in the example itself, it's opinion. But the presenter is attempting a heavily bias Loaded/Leading/Complex Question fallacy.

Person 1 is expressing an opinion "violence is wrong" with a criticism of the "tu quoque" fallacy implied by 'fighting fire with fire' phrasing of the question.
Person 2 is using "special pleading" to justify 'fighting fire with fire', with the implied argument from ignorance "what else can one do"