I find it troublesome that we do not call the Shias the unbelievers but on the other hand why do we exclude the 5th Imam Jafar?
By the definition of the Qur'an (9:11) as long as a group of people consider themselves Muslims, believe in God and his last Messenger and pray and pay Zakah like the rest of the Muslims then they are Muslims. This definitely includes Imami Shia Muslims.
As for including or excluding Imam Jafar al-Sadiq, this has no real meaning. Any one is free to take benefit of the views of any scholar of the past. At one point the state of Muslims decided to announce the 4 Feqhi schools of Hanafi, Maliki, Shafe'i and Hanbali as the the 4 official ones. This is simply a man made decision hugely influenced by the political and social circumstances of the time. Many other Feqhi schools of thought were excluded in this man made decision, including the Jafari Feqhi school of thought. This by no means implies that they or their followers were considered or are considered as non-Muslims.
In fact it is reported that the renowned head of the Al-Azhar University in Egypt, Sheikh Mahmoud Shaltut, in 1378 a.h. issued a Fatwa where he formally announced that following the Jafari Feqhi school of thought is permissible and that the religion of God and its instructions are not exclusive to any particular school of thought.