Did Elthina do the right thing by staying neutral?

No he didn' t say that he asid he did it because he felt there wasn't going to be one or at least that's how I interpreteted it. Because if ther ewas going t obe a compromised by that point Elthina would and should have offered it

You're joking. Elthina's compromise isn't compromise.

Did you hear, what she said to the templars in the beginning of Act 1, when she ordered them to escort Orsino back to the Circle? "Gently, pls!"

I'm sure, you think, this is a proof, how nice is Elthina, how cares about the mages. But no. She said it, because she knew, the practice is totally different – and wanted to show, how merciful is her. In this scene, she proved, she support Meredith. 
Yes, she sent Meredith back to the Circle – aw, but this is equal treatment!
No.
With this "equal"treatment she proved, she stands by Meredith and her methods. 

Not mentioned: at the moment, if she sends them both back to the Circle again – Meredith would continue her horror, and not many times later, Annul the Circle. Behid the closed door. But her hands remains clean, isn't? She proved, she's "neutral" and always so kind!

Not Anders took the compromise away. But you right about it, that was never compromise. He still hoped for the last moment. 
You cited Anders, so I'll too:
"No. Talk of mages! Give her one final chance to hear what we have suffered to pick a side. Perhaps, she will more inclined to listen to you." In his personal quest...
And what a surprise: She was not able to listen Hawke.

No, I don't believe such a thing, but you believe, that the lobotomy is a mercy. Wants to continue that, or you able to be civil? I would appreciate...

What he meant was that any "compromise" would have meant going right back to the atrocious status quo, since Elthina clearly has no interest in actually getting her subordinates under control and making them obey their own laws. Besides that, Elthina only delayed the Annulment. If Karras is alive in Act 3, he states that Meredith went over Elthina's head and directly petitioned Divine Justinia for the Right. Since Elthina opted to lie to Leliana, Justinia's only information would have Meredith's heavily distorted account. The moment Justinia's answer came it would have been out of Elthina's hands.

The third time the Right of Annulment was used, Knight-Commander Gervasio faked an uncontrollable demon infestation to hide the fact that his Knight-Captain was killing mages out of pure bigotry. Though Knight-Captain Nicholas was eventually dealt with by the Seekers, the truth remained hidden from the rest of the Circle of Magi, and the status quo kept right on going despite such a blatant example of what was wrong with it. By provoking Meredith into jumping the gun instead of waiting for permission from Justinia, Anders single-handedly stopped history from repeating itself at the Gallows.

Leliana was not here to investigate Meredith's sins. She was there to investigate the blood mage and Resolutionist presence in Kirkwall. Nothing about the Templars. Also, Elthina probably painted the situation absolutely okay in the Circle. Leliana supposed the danger come from the mages, Tevinter, not from the Knight-Commander of Kirkwall.

What about your Justinia? She honored what Celene did in the Alienage. There was no compromise, yes? Some murders are okay? Some murderers are okay?

Well, as you said, that's not what "compromise" means, thus Anders's statement that "there is no compromise." Elthina certainly wasn't offering a real one considering her refusal to do anything about Meredith's blatant law-breaking.

Leliana makes no mention of the Templars' misdeeds during her investigation. She's focused entirely on the Resolutionists. If her report to Justinia were to include anything about Meredith being out of control, it would have come up during her appearance, yet it is conspicuous in its absence. Combined with Elthina's lies, that leaves Justinia only with Meredith's twisted version of the situation. Besides that, Justinia's support for the mages didn't prevent the Annulment of Dairsmuid while the Nevarran Accord was still in effect.

Exactl yElthina wasn't tasking any action whic hwhy Anders felt he had to. I'm no tasyin geither side is righ t o rwron gin wha tthe yudid but I certainly can see why Anders felt the way he did and why he took the actions he did even if he was going to be executed for it.

That's because the game needs to account for the possibility that Karras is dead. Considering he's one step behind Alrik, a lot of people are going to kill him when they get the chance. But the fact remains that Hawke can directly hear from Karras that Meredith has sent for the Annulment, and Anders can be in the party when that happens. 

Elthina told Hawke to tell Leliana that the situation wasn't as bad as it seemed. She lied by omission about Meredith's extensive crimes that were directly responsible for the current situation. We know this because Leliana never mentions Meredith's crimes; she's focused only on the Resolutionists.

Meredith's convictions about the presence of "blood mages" does not grant her the right to decide that an entire Circle needs to be wiped out on a whim. Meredith didn't have to Annul the Circle in response to Anders's crime. There was absolutely nothing stopping her from taking him into custody and executing him for what he did, especially since she knew that he was never a resident of the Gallows. The Annulment of the Gallows was at least as much of an atrocity as the chantry explosion, and it is one that Meredith chose to commit. That is was Anders meant when he said that the world needs to see that the Circle is not a solution. They both committed an atrocity. His was committed for the purpose of exposing hers.

Both are acts of mass murder of innocent t people. They are equal evils. Only idiots or psychopaths think differently.