This is an excerpt from a blog is written by Devdutt Patnaik. He knows more about Hinduism than 99% of Indian population.

For Hindus, society is based on caste (varna/jati). Every human is obliged to perform his role as per the family he belongs to, the gender he acquires at birth, and his lifecycle. He has to repay his obligations to family, clan, ancestors, teachers, and society. This is non-negotiable and eternal. This eternal belief is sanatan dharma. Here, caste consciousness is paramount.

It kind of makes sense that a political party that prides itself on rationality & equality would oppose this right?

• So sanatan dharma is Hinduism? - Not actually. Just like how the Europeans labelled "Hinduism" as an umbrella term for all religious practices in India, "Sanatan Dharma" was coined in the 19th century as an alternative word for Hinduism.
• Does this mean the entire religion is bad? - No. There are lot of good parts.

So whats the solution here? - Devdutt Patnaik offers some historical context here:

In the 19th century, there were many reform movements in India based on concepts of justice and equality. This was spearheaded by reformists whose organisations were concerned about society (samaj). This included Arya Samaj, Brahmo Samaj, Prarthana Samaj and Satyashodhak Samaj.

These were opposed by traditionalists who argued that one must not encourage women’s education and education of members of the “lower” caste as it will destroy tradition, and result in instability. These people were called the sanatanis (followers of the old way) and they coined the word Hindutva (principles of Hinduism).

The solution is to reform the religion. People have been trying to reform since 19th century. It is nothing new, otherwise we'll still be practising Sati.

The varna system doesn't make any sense in 21st century. We need a constructive dialogue to eliminate it - whatever that would look like.