I get that for whistleblowers, journalists, investigators, ... I don't think it's relevant for a birthday party with children.
If it's me, I'm leaving the party. If it's my children attending, I'm strongly recommending them to leave the party (or just leave with them, depending on their age). Live-streaming a birthday party of children is obnoxious behavior that should not be tolerated.
This is the case where I find law in Europe better than USA. In germany you need consent to film or record other people.
The downside is the misuse of the law, what happens constantly, to basically prohibit (at least in practice) ANY recording activity. Is not unheard of, I have seen and experienced myself quite a few times, for example, a tourist being stopped and asked to delete a video of a simple recording in a park (police called immediately), because a random stupid person was around and wants to show how good he knows his rights… (see sister comment)
If it’s me, in Germany, I would instantly tell this person to stop filming and to delete any recordings. And if they streamed live to expect a letter from the (German equivalent of the) DA soon, as I would - as soon as back home - I would press charges and search damages.
Because in German publishing images/recordings of an individual without consent violates basic constitutional rights. And that’s nothing to f** with.
If minors were involved you’d be in a whole different can of soup even.
So while I don’t advocate for violence - as others have hinted in this thread - a black eye could actually be the lesser negative outcome for such a person.
If it's me, I'm leaving the party. If it's my children attending, I'm strongly recommending them to leave the party (or just leave with them, depending on their age). Live-streaming a birthday party of children is obnoxious behavior that should not be tolerated.