I know Jains do not accept the authority of the Vedas. But what are the main theological differences between Hinduism and Jainism?
One difference I am aware of is their views on reincarnation. Though they both believe in reincarnation, they differ on the minor but crucial aspects of the process.
Hinduism believes that during the death of the body, atman collects itself and carries with it the mind and its latent tendencies that becomes the seed of the next life. In support of this view, I am quoting the following famous verses from Brihadaranyaka Upanishad. [BU]
The soul of the unreleased after death
"Now as a caterpillar, when it has come to the end of a blade of grass, in taking the next step draws itself together towards it, just so this soul in taking the next step strikes down this body, dispels its ignorance and draws itself together [for making the transition]." BU - 4.4.3
"As a goldsmith, taking a piece of gold, reduces it to another newer and more beautiful form, just so this soul, striking down this body and dispelling its ignorance, makes for itself another newer and more beautiful form like that either of the fathers, or of the Gandharvas, or of the gods, or of Prajapati, or of Brahma, or of other beings." BU-4.4.4
"... According as one acts, according as one conducts himself, so does he become. The doer of good becomes good. The doer of evil becomes evil. One becomes virtuous by virtuous action, bad by bad action." BU - 4.4.5
"On this point there is this verse- Where one's mind is attached - the inner self Goes thereto with action, being attached to it alone. Obtaining the end of his action, Whatever he does in this world, He comes again from that world To this world of action." BU- 4.4.6
Because of this view, in Hinduism great stress is given on what one thinks in his last moment. Hindus chant the name of Rama and try to calm his mind and create a peaceful atmosphere for that person.
Whereas, Jainism believes atman leaves the body without taking anything from previous lives. So it moves from one life to another just like a parrot moves from one tree to another, no strings attached!