Did Elthina do the right thing by staying neutral?

She was considering an Exalted March on the whole city. In fact, had the DLC not been cancelled, that is precisely what would have happened. So it doesn't seem that much of a stretch that Justinia would have agreed to the Annulment if Meredith put forward a decent enough case for it. As I've said before, it seems likely that Leliana was sent to Kirkwall in order to check out the situation so Justinia could decide what to do. Since she is advising Elthina to get out whilst she can, it does seem as though the report is not going to be favourable.   If the Veil is known to be so thin there it is likely to give her more reason to allow it since Meredith could argue too many demons are getting through and corrupting the mages.

Justinia is happy to bring about reform on her terms. However, Cassandra says that Leliana is wrong to think that Justinia would have gone as far as freeing the mages entirely. When she helped the mages escape the White Spire I think she thought it wouldn't be long before they saw sense and then surrendered on her terms. In fact she sends peace overtures to them at Andoral's Reach. When Fiona is putting this to the vote she says that they will be surrendering to the Divine's mercy and no doubt some heads would have to roll in order for Justinia to save face. They would be going back to reformed Circles but still under the control of the Divine, which is what Cassandra institutes if she is Divine. As Justinia authorised the new Cumberland Chant of Light, which includes the Canticle of Shartan, it would seem restoring that was something she wanted to do but likely that would be as far as reforms within the Chantry went and she would not have authorised all races and sexes becoming ranking clergy rather than just brothers and sisters.

Leliana is the one who completely changes the Chantry, so to a large extent it is no longer the Chantry that Drakon instituted. In some ways, the Chantry under her rule may actually be closer to how the faith was immediately after Andraste's death. As Leliana was Ferelden born, initially raised there and then returned there as a Chantry sister after her negative experiences with Majorlaine, I do wonder if she picked up some other native ideas on the faith, say from the Ash Warriors, for example. We never get to learn exactly how their faith in the Maker differed from that of the Chantry but it had to have been different since the codex about it says they do not acknowledge the authority of either the Chantry or their Chant of Light. Since the Ash Warriors were converted by Gelgennig before the existence of the Orlesian Chantry, it would seem the Ash Warrior's faith must have been closer to the original faith of Andraste, particularly considering they came from the same country. It is annoying they largely killed them off at Ostagar so we never really learn what they believed apart from in those brief codex entries.

Lol, "reform" never actually translates to any meaningful progress or change. What was Justinia ACTUALLY going to do? Institute voluntary sensitivity training?

"Okay, now, if you see a mage practising spells alone at night, what is the appropriate response to that situation?"

"Um... rape them?"

"Close, but not quite! First, it is appropriate to ask them what they're doing outside of the dormitory past curfew. Then, if you don't like their answer, check to make sure that they aren't dating Bastien de Ghyslain, and if they aren't, THEN you can rape them."

And if she was sooooooo concerned about avoiding mass violence in Kirkwall because of the thin veil there (which like, is that even common knowledge? We only know it because of an obscure codex entry), then why didn't she... I dunno, rein Meredith in when she overstepped her bounds and seized control of the city?

Because the Grand Cleric matters, politically – the others just nothing: just pawns on the big chessboard in the eyes of the Chantry's leadership.
Yes. 
This is a surprise? We speak about an Exalted March, against the city... (including the citizens of the city) and a danger of the whole city, and the Divine wants to protect the only person who matters – politically. This is the Chantry's value exactly.

Elthina isn't just Grand Cleric of Kirkwall but the whole of the Freemarches. Kirkwall is just her base. Thus the Divine would consider it important to ensure her safety because of the impact on he rest of the area if anything should happen to her. Elthina can continue to issue edicts and encourage calm in the other city states whilst the Divine embarks on her Exalted March against Kirkwall. I would imagine the rule is to protect the interests of the Chantry above all else. This is why she never took any action to remove Meredith from her position or instruct her to relinquish control of the city to the secular authorities. Essentially both Elthina and the Divine were in favour of the Templars controlling the city because it emphasised the power of the Chantry over every aspect of citizens lives.   If the city seems to have grown worse under the rule of the Templars, simply blame it on the mages and subversives, not on the fact that they shouldn't be involving themselves in secular governance.

Well the Divine would argue that their authority is contained in the Chant of Light. That is what is used to justify everything that they do in the name of Andraste. The fact that there is nothing in the Chant of Light to support their position or it is open to interpretation does not deter them. The Divine doesn't need any other written rules, just insists they are doing the Maker's will. It is the same with Orlesian nobility. They rule by Divine Right so to rebel against their authority is effectively a sin and of course they also see it as licence to do as they please.