By very design, Hinduism has multiple facets, multiple ways to approach God within its overall scope. The religion offers the freedom of choice, freedom of expression, freedom of dissent and so on. Naturally, it gives religious people freedom to compartmentalize themselves, disagree with other sects, argue with them, demean them etc. Sri Ramakrishna Paramahamsa says even atheism is a stepping stone to reach God in Hinduism!
I would say that the absence of unity in Hinduism is exactly like feuds within brothers and sisters in a family! They may not see eye to eye with each other, have different tastes and agendas in life, may even split from the family and live alone. But the underlying blood connection never goes. When some calamities strike the family, we can see that all family members bury their difference of opinions and come together!
In a similar way, there are indeed occasions when Hindus reunite burying their differences of opinions and tastes because the underlying concept of God is fundamentally same amid the various sects, irrespective of whether people comprehend them fully or not.
Hindus as a society do face problems and differences because of caste system; but again, history shows that our religion is not rigid, but flexible enough to acknowledge and take corrective actions in the long haul. Where there is lack of unity, it is mostly fueled and nurtured by petty politicians who have little deeper knowledge about Hinduism; they bet on their pseudo-secularism to keep dividing Hindu people for their selfish gains.
On top of it all, please consider this:
Historically, how much of bloodshed have you seen amidst Hindus fighting within themselves based on their religious differences? Extremely little.
Compare this with the history of other religions: Shias versus Sunnis; Protestants versus Catholics.
Then the reality will be far clearer.