Please don't think that you can stop a Nazi by pointing out hypocrisy or by pointing out that they are lying.
They know. It is a feature, not a bug.
When a fascist lies to you, they are displaying power. "I know I am lying. You know I am lying. What the fuck are you going to do about it."
When a fascist lies to other fascists, they are displaying loyalty. "I know I am lying. You know I am lying. We do this because it is how we show allegiance to the cause."
In this way, fascism is inherently an empty ideology. It stands for nothing. It believes in nothing. It can therefore lie about everything.
Except one thing: power.
Fascism MUST lie. It MUST deceive. It MUST play to baser beliefs like racism, sexism, homophobia, transphobia and xenophobia, because it has literally nothing of value to offer.
They know this. We know this. That is why they lie.