As you've no doubt seen on recent threads, this is a contentious issue with multiple viewpoints. However, one clarification I can make to your question that I think most sides would agree with:
There is a difference between 'recognizing group X as Orthodox' and 'recognizing group X as autocephalous (or a number of other administrative distinctions'. The first refers to whether or not the group is part of the Church, and there is actually generally very broad agreement on that in almost all cases. The second refers attitudes towards certain administrative issues--on the one hand there are a lot more controversies in this field, on the other hand, they are a lot less important than the first idea, which is part of why they linger so long.
To use the OCA as an example--The Patriarch of Constantinople, the Patriarch of Antioch, the Patriarch of Moscow and every bishop and layman in communion with those all recognize the OCA as Orthodox. Where they differ is on the administrative status of the OCA.
- The Patriarch of Moscow says that the OCA is a self-ruled Church, meaning it elects its own Metropolitan and has no higher authority other than a General Council; Moscow also says that the OCA is the 'canonical' church for North America meaning that all non OCA-clergy should get the OCA's permission before being active here.
- The Patriarch of Constantinople says that the OCA is a portion of the Patriarchate of Moscow. That whether the Russion Synod chooses to exercise it or not, it has authority over the OCA's choice of bishops, etc. And that neither Moscow nor the OCA are the canonical authority for North America.
- Other autocephalous churches take positions ranging between the two extremes of Moscow and Constantinople.
This is an intentional simplification, there is lots of history and more complications, but it gets at the basic disagreement. But everybody does recognize the OCA as Orthodox, meaning they will give communion to OCA members, will receive communion from OCA clergy, and will concelebrate with them.
Now, in addition to the administrative disagreements above, there are two major divisions where the issue of 'is the Church' actually comes into being:
1) There are a group of churches, generally known as 'Old Calendrist', who have separated themselves from what they sometimes refer to as 'World Orthodoxy' (meaning all the Patriarchates and the Orthodox in communion with them). I won't try to speak for them--there are multiple members of this group on this board who can address as they see fit--but generally the main body of Orthodoxy consider them to be in schism, and they consider the main body of Orthodoxy to no longer be Orthodox.
2) There are several groups, such as the Macedonian Orthodox Church, one of the Ukrainian Churches, etc which have split without authorization from their traditional synod (generally for nationalist reasons). These are out-of-communion with the rest of Orthodoxy and are considered in schism, although they seek recognition as new autocephalous entities.