I think that both political vitriol and the mental illness played a part in this, but I think that the critical cause - the 'but for' factor without which the crime wouldn't have occurred - is the mental illness. I look at it this way: with no mental illness, a potential assassin is going to consider the possible consequences of their actions. He or she may decide that it's 'worth it', but there is going to be a period of premeditation. Also, a premeditated assassination is more likely to go for the target, and once the target is dropped, the assassin would consider the mission 'accomplished', instead of continuing to shoot.
With a mental illness in the mix, that premeditation may not occur at all, or may be distorted beyond any rationalizing. Hinckley tried to kill Reagan because he thought it would make Jodie Foster fall in love with him. JLL's motives could have been influenced by the political vitriol or by his own personal demons. The vitriol didn't help matters, but I can't see it as the root cause.