I think that you will find that the sects of Hinduism are not entirely ingrained and embedded in the Hinduist school of thought. A religion that is as old as Hinduism is bound to have some different interpretations and this might be where the issue of sects arise. For the most part, the development of different sects comes out of in what primary deity one believes. For example, the Vaishnavite sect are primarily devotees of Vishnu, and show a preference to him. At the same time, the Shavite sect pledges their allegiance to Shiva. The vision that is believed in by those who believe in Shakthism is where the role of the Goddess Shakthi is evident. I do believe that you will find within each sect there are different premises and beliefs. The individual preference that one has or that one's family might possess helps to bring out the division on the grounds of sect to be evident.
However, I think that two elements should be noted. The first is that I don't think any Vedic literature or Puranic text embeds these divisions as a necessary part of the literature and worship. There are many instances where, for example, Vishnu and Shiva are extremely close to one another, almost indistinguishable. For example, there can be instances seen in the narrative where Shiva runs to Vishnu for help and for guidance. This is also seen when Lord Rama, an avatar of Vishnu, must pray and give obeisance to Lord Shiva before and after killing Ravana. When Lord Krishna assumes his Vishwaroopam form in front of Arjuna in order to give him confidence and strength, it is done to bring unity, enhanced by the fact that Arjuna sees that "Krishna is Shiva and Shiva is Krishna." When the goddess Kali seeks to destroy in order to bring balance, she is only assuaged by stepping on the body of her husband, Lord Shiva, a sign that he is the unifying force with her that provides the balance to creation and destruction. Lord Vishnu is shown to give obedience and complete submission before a particular version of Lord Ganesh, one in which his elephant trunk is situated to the right side. This becomes particularly poignant when one realizes that Lord Ganesh is the child of Goddess Parvati, embodiment of Shakthi, and Lord Shiva. Finally, both Lords Shiva and Vishnu hold Hanuman in high regard and in esteemed position, almost bringing both together. While the sects and preferences do exist, I don't see that there is anything within the large body of literature to suggest that the sects are not subdued by a larger worship of the religion.
The second point to be made here is that the polytheistic element of the religion brings to light how sect division is not one of mutual exclusivity. It is here where I think that the challenge of understanding Hinduism is most evident. The notion of the mere word of "sect" brings about images of competition and destruction. "Sectarian violence" or "sectarian rejection" are examples of this. Yet, Hinduism really wishes to bring to light the idea that divisions and multiplicity are not elements that are mutually exclusive to one another. There is a way for individuals to be able to embrace division, and foster a sense of grasping complexity without being challenged or put off by it. In this, one of the most profound lessons of the religion is on display for the devotee.