Charged versus rotating black holes as different kinds of wormholes I've heard that a maximally extended charged black hole can be a traversable wormhole to the same universe whereas a maximally extended uncharged rotating black hole can only be a wormhole to different exteriors that are merely isometric regions of spacetime.
Now I want to ignore whether that is correct. (So ignore the issue that differential geometry allows transition maps between local charts so you can obviously identify two sufficiently isometric regions by just connecting one to the other by appropriate transition maps.)
What I am interested in is what is the basis for a potentially infinitesimal amount of charge changing so fundamentally whether the isometric regions exterior to the black hole are the same universe or different universe?
Specifically, how would that happen, how could that happen? And to do it you might have to distinguish the two possibilities, which might require not ignoring the fact that you can clearly identify them.
But I am trying to ask how charge can do that? And how anything could do it? And what would  required to assert the two isometric solutions are different?  For instance if you look at the Penrose diagram you could just translate the diagram upwards and identify all the parts.
 A: 
Charged versus rotating black holes as different kinds of wormholes

There are no wormholes Timaeus. And no time travel either. There is no magic. Sorry.  

I've heard that a maximally extended charged black hole can be a traversable wormhole to the same universe

And I've heard that when you die you go to heaven. Only I know that my fable isn't true. You should know that yours isn't either, because you know that the coordinate speed of light at the event horizon is zero. That's the speed of light as measured from afar by a distant observer such as me. And we both know that matter cannot exceed the speed of light. So when you try to traverse what you've heard is a wormhole, you grind to a halt. Make sure you read Kevin Brown's Formation and Growth of Black Holes and pay attention to the frozen-star "field interpretation". The alternative interpretation (which is the one popularized by Wheeler) requires a trip to future infinity and beyond. That hasn't happened yet, and it never ever will. Quite apart from that, there are issues with charged black holes, and with  firewalls.    

whereas a maximally extended uncharged rotating black hole can only be a wormhole to different exteriors that are merely isometric regions of spacetime.

On top of the above, there are further issues with rotating black holes. See this article: Monster Black Hole Spins at Half the Speed of Light. What's the coordinate speed of light at the event horizon? And what's half of that? Problems, problems problems, and it all stems from the simple fact that the descending photon slows down. 

Now I want to ignore whether that is correct. (So ignore the issue that differential geometry allows transition maps between local charts so you can obviously identify two sufficiently isometric regions by just connecting one to the other by appropriate transition maps).

Another thing you need to ignore is the fact that there's no motion in spacetime. See Ben Crowell's answer here. Spacetime is not what space is. You move through space, not through spacetime. So Penrose diagrams are science fiction I'm afraid. It's like thinking the door to the furnace leads to eternal paradise.  

What I am interested in is what is the basis for a potentially infinitesimal amount of charge changing so fundamentally whether the isometric regions exterior to the black hole are the same universe or different universe?

What you should be interested in is what happens when you chuck an electron into a black hole. FriedWardt Winterberg says it gets ripped into gamma radiation. I think he's right. Note that we have no evidence of wormholes, but we do have evidence of gamma ray bursts. 

Specifically, how would that happen, how could that happen? And to do it you might have to distinguish the two possibilities, which might require not ignoring the fact that you can clearly identify them.

I think it's a fantasy, Timaeus. Sorry. That electrons falls down because the "coordinate" speed of light is reducing. The electron falls faster and faster and faster, and there comes a point when it would be falling faster than the coordinate speed of light at that location. That just isn't going to happen. Something's got to give, and that something is the electron.   

But I am trying to ask how charge can do that? And how anything could do it? And what would required to assert the two isometric solutions are different? For instance if you look at the Penrose diagram you could just translate the diagram upwards and identify all the parts.

Ah, the Penrose diagram. I'm afraid it's all fantasy. There is no Einstein-Rosen bridge to another universe. All that was ever about was particles. Read the paper.   
