I think you are talking about
A camel
They say I'm a ship
A camel is also called as the "ship of the desert"
But I see no water for days
There is no water in their habitat, the desert
You may think you know me From my cousin of holy ways
The cousin of the camel is the llama. Llama ( Lama ) is a reference to Dalai Lama, the Buddhist Monk.
Look for me in abandoned places
A desert is pretty abandoned.
And you might find an obstacle or two Its what keeps me going long When the movers move
As Kevin Rubin has stated, " 'an obstacle or two' could be the camels' humps. These humps store water for the camel which helps them going long. "When the movers move" could mean the camel herders because they "move" the camel around by riding it.