The article did state that expressing desire for violence could be enough to get your children taken from you. Merely stating that you want to kick out all of the refugees wouldn't be punished aside from the obvious social and workplace implications that it could come with it.

"Expressing a desire for violence against the migrants would constitute evidence enough for a family court to remove children from the home, according to Becker."

Now, if that includes all racist or anti-migrant comments, then of course this is a completely different thing.

I have different standards for Facebook and VGC because they are different platforms with different audiences and with a different history of censorship. Apples to oranges. While I recognize Facebook's right to censor content, I will decide not to use their website if they started to censor at a large-scale effort. 

Except child porn actually involved the action of child molestation/rape to produce, while expressing anti-immigrant sentiment does not mean you are enacting what you say or feel. The real equivalent would be if the government started to get involved if somebody declared oneself as a pedophile (but not one who harmed.) 

First, it's about how you say it. On VGC or elsewhere. If you posted the same exact sentence on FB as you did here, there wouldn't be a problem.
Second, I didn't say that it's the same as someone who had sex with children or someone who makes pictures or videos about sexual abuse of children. I was merely saying "someone who posts child porn (on Facebook or anywhere else on the internet)".
Quite comparable.

I think Germany has taken their censorship way too far. I understand their history and why they feel the need to combat hate speech but this isn't the right approach. Banning hate speech, getting rid of anything that is remotely hateful or may lead to hateful rhetoric will not get rid of the hate. A better solution would be to call people out on their bullshit.

Also, how far will this go? How long is it before Germany consider any criticism of the government to be hateful speech?

But openly admitting that you're a pedophile is not a crime in itself. Incitement of the people on the other hand is (in Germany and some other countries).
Someone who "merely" owns and posts child porn also isn't accused for the child molestation but for owning and spreading the illegal media (=information).
And that is again very comparable to the topic.

I think it depends on the statement. If it's just someone expressing their discontent about the situation then it's fine but if the comment amounts to a death threat or inciting violence against the refugees then the person should be reported to the police.

To me, stating a desire to kick out refugees would be enough to qualify for violence against, because there's no way in hell they're going back on their own.

I doubt a court would or could think the same way. Well, they might think the same way regarding that there's no way they're going back on their own, but I don't think they'd equate a desire to kick them out to a desire for violence against them.

But from the sounds of the OP it goes beyond incitement. There is a difference between desiring harm against someone and telling others to do it. Just as there is a difference between desiring sexual intercourse with a child and promoting the harm of children by purchasing content that was produced through the harm of the child. 

"Becker suggests that racist and xenophobic statements made in the presence of a child that constitute a “negative influence” would also be investigated by the authorities."

"Expressing a desire for violence against the migrants would constitute evidence enough for a family court to remove children from the home, according to Becker."

No matter your political inclination, I think anyone who supports a democratic regime and the freedom it entails should be really careful on censoring and criminalizing the conduct of others. I don't think most of us need to be reminded that history basically works itself in circles, so the same strategy you know use to censor and criminalize a certain point of view, might be come to be used against you in the future.

As for punishing someone for threats of violence. That's what the doctrine calls crimes of abstract danger. Or, in the German Crimnal Law, abstrakt Gefährdungsdelikte. It comes from the fallacious, outdated notion of a victimless crime and restraining the freedom of someone based on the presumption of danger. One would think the Grundgesetz should protect people against the barbaric notion of punishment against abstract danger, but it is long since the Grundgesetz stopped being a warranty against the arbitrariness of Government to become a tool of its ideological inclinations. Basically making the mistake I pointed out on my first paragraph.

What Germany needs, if it wants to still be called a land of democratic rule of law, and remind people of the dangers of an unchecked nation against a minority, is better politics of memory, not punishment, because that's counterproductive at least, and can even be considered downright incoherent and paradoxal. I've written elsewhere once on how the politics of memory on Germany are all about WW2 guilt to the point of being psychological terrorism instead of a reasonable discussion on the limits of State. On other words, ein totales Scheiß.