The main problem today is that we have to choose how to understand and live Islam. While some matters are essentially trivial (such as whether to hold the hands up or down when praying), there are some significant differences between Sunni and Shi'i theology, and worldviews, sometimes on basic questions such as free will and predestination. There are also differences of opinion about communal religious practice, such as whether it is acceptable/desrirable to recite du'a as a group or pray taraweeh prayers together. 

Sunnis and Shi'is also have markedly different hadith collections. Yes there are some similarities but there are also some significant differences in approach. So there are differences in the sources used to understand the faith.

So, because Islam has branched off into different understandings, it is necessary for a Muslim to adopt some understanding, ideally the one that sh/he thinks is the truest. While it is possible to respect everyone, it isn't possible to agree with everyone about everything; at some point you have to either make up your mind on some issues. 

However I think it is better to focus on trying to find out what is true and do what Allah and the Prophet would intend, rather than to focus on matters of identity. There is usually some truth to be found everywhere. 

From a Shi'i perspective, the concept of being one of the followers of 'Ali (Shi'at 'Ali) does trace back to the utterances and time of the Prophet, so it was not a new idea that came later.