Certainly, there are some beliefs and teaching that are common to all, ie the Blessed Trinity, the life, death and resurrection of Christ, etc.
What are the official teachings of Eastern Orthodoxy - those matters agreed upon as being essential to the Faith - that are absolutely irreconcilable with the essential teachings of Roman Catholicism?
There are certain practices that the EO regard as acceptable, but we Catholics must reject them as gravely immoral. These practices, if done with full kowledge of the fact that they are sinful, qualify as mortal sins and are sufficient for the eternal damnation of the soul. The ones I know are artificial birth control (ABC) and ecclesiastical divorce.
ABC is forbidden as gravely immoral by the CC - this includes condoms, surgical procedures such as vasectomy (men) and tubal ligation (women), the pill, intrauterine devices etc. Most EOC allow ABC as long as it doesn’t cause abortion. For example, a married couple may receive their EO priest’s blessing to go ahead and have a surgical procedure that will render either the man or the wife permanently sterile (vasectomy, or tubal ligation).
Regarding ecclesiastical divorce, which is allowed by the EOC, the CC teaches that a validly contracted and consummated marriage can never be dissolved as long as the parties are alive - it will only cease to exist when one of them dies.
There are certain teachings (dogmas) that all Catholics must believe under pain of excommunication. Those are the dogmas that are solemnly defined by the CC, followed by a formula such as “and if anyone shall say that this is not true, let him be anathema”. Some of those dogmas that were solemnly defined by the CC and all Catholics must believe them, but are rejected by the EOC, include the role of the Pope as supreme leader of the Church, the existence of the Purgatory, the Immaculate Conception of Mary, and the Assumption of Mary, body and soul, into heaven.
Here’s what the CC teaches about the Pope, things that are rejected by the EO: that the Pope is infallible (cannot fall into error) when teaching ex cathedra on matters of faith and morals. That when the Pope defines teachings on faith and morals, ex cathedra, his teachings are definitive and irreformable - that is, nobody can change, question or reject these teachings, and furthermore, the Pope doesn’t need the approval of anyone else, such as the faithful at large, or the rest of the Bishops, gathered in an Ecumenical Council, to “approve” these teachings. The Pope also has a veto power over the decisions of Church councils, including local Councils and Ecumenical Councils (councils of the Church Universal). Moreover, the Pope has “immediate and ordinary jurisdiction” over the whole Church. This means, for example, that the Pope can depose and excommunicate a Bishop who has fallen into heresy, not only in his diocese of Rome, but anywhere on the globe. We Catholics must believe (we are not free to reject) that the Pope was given all this authority by Jesus Christ, that he exercises his God-given, legitimate authority when he infallibly defines teachings on faith and morals, and when he exercises his immediate and ordinary jurisdiction over the whole Church. However, the EO reject all of this - they do not believe that the Pope can infallibly define teachings on matters of faith and morals, or that he has the right to exercise immediate and ordinary jurisdiction over the whole Church, beyond his diocese of Rome.
We also must reject the EO view that the “filioque” is a heresy, and that the CC has fallen into heresy by adding the filioque to the Latin text of the Creed (filioque = “and from the Son”; see the Creed where we recite that the Holy Spirit proceeds from the Father
and from the Son). The EO believe that the teaching Magisterium of our Church has fallen into heresy, and that our Popes had upheld a heretic teaching for many centuries. But we reject the notion that our Church taught, and continues to teach, heresy.
All Catholics must believe that the CC has valid sacraments, including valid baptism and valid Eucharist. Thus we must reject the beliefs of those EOC who say that our baptism is not effective to salvation, or that when Catholic priests consecrate the bread and wine, it doesn’t truly become the Body and Blood, Soul and Divinity of Jesus Christ.
Whenever the CC officially canonizes someone, it means the Church infallibly discerned that the person is in heaven. Thus we Catholics must believe that our canonized saints, such as St. Francis of Assisi, St. Anthony of Padua, St. Catherine of Siena, St. Teresa of Avila, St. Therese Lisieux, St. Pio (Padre Pio), and others, are truly in heaven. When the EOC makes fun of and mocks our saints, I strongly suspect they don’t believe that infallible discernment of our Church that these saints are for sure, beyond the shadow of a doubt, in Heaven.
When the CC judges that a certain Marian apparition, e.g. the apparition at Guadalupe (Mexico, 1531), Lourdes (France, 1858) or Fatima (Portugal, 1917) is “worthy of belief”, it means we definitely do not err by believing that Mary truly appeared there, although we are not
required to believe it. So, when the EOC do not believe these Marian apparitions, they are within their right not to believe them. However, they go beyond that and some of them mock those of us who believe them, even though our CC determined that the apparitions are worthy of belief.
Regarding various matters of Church discipline, such as the use of the New Calendar (Gregorian calendar) by CC, the presence of pews and musical instruments in churches, the use of unleavened bread for the Eucharist, the shaving of beards and tonsures by Catholic clergy, we Catholics can simply trust the authority of our Church to do these things, which means we reject the EO opinion that we are heretics for doing those things.