On the off chance that the ultimate cookie is made in the bad batch au, then earthbread is doomed, I don’t think bad batch Gingerbrave would do anything to help
Well, honestly, that depends.
BB!Gingerbrave believes in an idea of Absolute Freedom. However, he isn't interested in destroying the world. He values his own life too much (and the lives of his friends) to just... let an apocalypse happen.
If something were to come along that genuinely threatens his and his friends abilities to have happy lives, then yeah he'd probably attempt to stop it.
He wants a world where he and his friends can be happy and do whatever they want. A world run by free will, and free will alone. This is why he doesn't like authority figures be they royalty or divine-like beings. He views them as getting in the way of free will by telling others what they can or cannot do. THAT is his main burn with a lot of the Ancients/Beasts/DE/etc. That is why he enjoys the idea of "anarchy".
The problem with his specific idea of freedom is that it is purely abstract and therefore unsustainable. If "freedom" means the simple act of imposing one's will, then it can be taken away by another imposing their will. (I.e. someone is free to make a corn field. now someone else is free to take that corn field from them, purely on a whim, and there would be no consequences or punishment unless it is carried out by the farmer who got his corn stolen alongside any who he recruits to help him.)
This, realistically, would turn the world into a war torn hellscape.
The reason he believes in this simple caricature of freedom is because... well... at the end of the day he's just a kid. He doesn't fully understand yet what it is that he truly wants. And because of his rebellious attitude thanks to his witch-based traumas, he's kinda going through the cookie equivalent of an angsty teen phase mixed with a bit of an existential crisis.
He wants to live. He wants to live happily. But he doesn't trust others. (Rather, he doesn't trust strangers who haven't proven themselves to him. How people initially react to him being undead plays a big part in this.) ((This is why he took a shining to Chili Pepper Cookie so quickly, because her initial reaction to him breaking his own arm off was asking if it hurt -- showing concern for his well being.))
He needs to understand that freedom isn't the ability to enact and impose one's will. But rather the ability to enact one's will while enabling others to enact theirs.
Basically: Individual Will vs. Solidarity