They don't hate Lord Ram per say, but they hate the idea that they will become powerless and a forgotten memory, if more and more people start returning to their roots and values embodied by this great figure.
Rajiv Gandhi was the leader of the most corrupt and incompetent government that India has ever seen. This is a reality and no, saying the same, does not amount to disrespecting the dead.
Since BJP is the only member based national party where power is not transferred within a single family, the process of transfer is more fluid. It is the party which decides when would the power be transferred and to whom.
This election is a clash between the views that "India was born in 1947" while on the other side we have the view that "India is a 5000 old civilization that got self-rule in 1947".
All that being said, an important aspect of all these practices -- Yoga, Kalaripayattu, Ayurveda, Siddha etc. is their strong roots in vedanta and Hinduism.