The Eastern Orthodox and the Oriental Orthodox were invited to the First Vatican Council as deliberative members.
The EOC refused the invitation because the invitation was couched in - to EO sensibilities - haughty terms.
Here is the text of Pio Nono’s letter:
“[W]e direct our voice to you, and with the greatest possible earnestness of soul we beseech, admonish, and pressingly exhort you to come to the said General Synod, as your ancestors came to the Councils of Lyons and of Florence; in order that the conditions of our former love may be renewed, and the peace of our Fathers may be once more called to vigour, so that the light of desired union may shine brightly upon all. Thus may continual thanksgiving be ever offered up to the Father of Mercies by all His Saints, and especially by those most glorious ancient Fathers and Doctors of the Eastern Churches, when from heaven they look down on the restoration and renewal of union with the Apostolic See, the centre of Catholic truth and unity, which they whilst living upon earth laboured with every effort and with unwearied toil to cherish, and daily to forward more and more by teaching and example.”
Here is their response:
“If His Holiness the Pope of Rome had respect to apostolic equality and brotherhood, it was fitting that, as an equal among equals in point of dignity, but being frist by canonical right and rank of his See, he should have directed a separate letter to each of the Patriachs and Synods of the East, and not in encyclical and dictatorial form to impose it as lord and master of them all, but as brother to brethren equal in honor and degree, to aske them how, where, and in what conditions, they would agree to the assembling of a Holy Council.”
Though the OO did not attend, I am not aware of any specifics regarding their lack of acceptance.
Blessings