Assyrian-tradition (Church of the East (COE)) Churches have long held that Nestorius was, to put it lightly, bullied by St. Cyril. Mar Bawai Soro, Chaldean Bishop, in 1986 said that, "A tumultuous council took place, with Cyril acting as both prosecutor and judge of Nestorius...

... The trial of Nestorius at Ephesus in which he was condemned has always been viewed by the COE as unfair and illegal. It should be noted that others, outside the COE and with impeccable credentials as orthodox scholars, have also agreed with that judgment...

... attributing the chaotic and embittered atmosphere at Ephesus to personal animus and political ambition on the part of Cyril."

What St. Cyril did wasn't a hashtag based attack on Nestorius. This was St. Cyril correctly having an issue with what we now call Nestorianism but wrongly attributing it to Nestorius, without first checking if he actually held the wrong Christological and Mariological views!

Check out these excerpts, below.

(DM if you want links to full papers.)

I could stop here. Nestorius wasn't himself Nestorian so venerating him isn't upholding Nestorianism, especially since the Churches that venerate him reject Nestorianism. All of their Christological and Mariological beliefs are apostolic and true. There is no heresy among them.

But to really drive this home, let me also add that the ACOE and the Catholic Church ratified that they share common beliefs in their apostolic Christologies in 1994.

http://www.vatican.va/roman_curia/pontifical_councils/chrstuni/documents/rc_pc_chrstuni_doc_11111994_assyrian-church_en.html

In fact, so strong is the partial communion between the ACOE and the Catholic Church that, in 2001, guidelines for members of the ACOE and the Chaldean Church to be able to commune at each other's Churches were established*.

http://www.vatican.va/roman_curia/pontifical_councils/chrstuni/documents/rc_pc_chrstuni_doc_20011025_chiesa-caldea-assira_en.html

*Ethnic Assyrians have faced persecution for centuries, and they are often displaced as part of that. Assyrians tend to emigrate to the same place; if and where that is not possible, they have the opportunity to receive the Eucharist at whichever COE-tradition Church is nearest.

The Assyrian-tradition Churches have always (literally for centuries) maintained what orthodox scholars figured out in the 20th century: Nestorius wasn't Nestorian lol.

If you're interested in reading more, Patriarch Sako of the Chaldean Church has written eloquently on it: https://saint-adday.com/?p=19438 

I’m rewriting this last tweet. The EOs online DO slander and, whether knowingly or by lack of motivation to actually look anything up, lie about the Catholic Church, but most EOs irl are very nice.