The vote bank of both left and BJP are Hindus. So they fear that the other will eat his cake, especially the left has that fear in Kerala. This is the root cause of conflict between the two - it is not ideology or secularism or communalism.
In most other similar cases, two parties having something in common will try to work together. It is impossible for Left and Cong to be toghther because in Kerala and to some extent in Bengal and Tripura, these two are the main parties of that state. The simple rule of coalition is that no coalition is possible at centre or state, between parties who are No1 and No2 parties in any State.
