Its the most natural thing for Hindus to want to reduce the focus on Muslim dynasties and focus on the Hindu ones. And this process of reducing Muslim cultural influence has been going on since 1800's well before BJP even existed.
Hindus and Muslims draw inspiration from different parts of subcontinent history. And the people who had the most impact on culture are the Kings and other ruling elites. So naturally Hindus will look towards Hindu and other pre-Islamic empires for their cultural symbols, while the Muslims will look at the Muslim Kingdoms.
The founding fathers of India & Pakistan were for the most part liberal, however one can look at the symbols of the state that India & Pakistan choose. The flags, motto's, the anthem, other cultural symbols, you can clearly see what inspired the selection.
And their is nothing wrong with this, and most Muslims accept that we draw inspiration from two different things. This is the essence of the two nation theory. However the problem is we are dealing with a very arrogant community, who cant accept this. For them Muslims must accept the Hindu point of view. Any difference is unacceptable, and is a result of them hating their own culture.
For these Hindus, Muslim who settled from outside the subcontinent are perpetual foreigners. Even though they were born and bred in the subcontinent and had married with local women, they still belong to Afghanistan, C Asia, Arabia, Iran, basically anywhere but the subcontinent. They believe that either they left the subcontinent, died, or a fringe community. The idea that they assimilated with locals is something they don't understand and are not capable of understanding. Mixture like what happened in Latin America, Middle East, England, etc is so alien to their culture, that they cant accept that.
And when they see a Muslim with what they perceive as a Hindu surname that's when the Bhangra starts for them. See look, and then proceed to explain the origin of the surname as if the person who has it wont know. The idea that this is not that important for people is difficult for them to understand. Kind of like how in England people have Celtic, Anglo-Saxon, Norman, etc surnames however no one really cares. Same way for Muslims its not that big of a deal. Social status is more important. For instance the surnames Butt & Bukhari indicates at one point the person in the male line would have an ancestor who was a Brahmin, & from C. Asia respectively. Their are Butt's & Bukharis who are rich, middle class, and poor. The rich will intermarry and socialize with one another, same for the middle class, and poor.
However among Hindus its very different. The chaprasi Brahmin, or the Rickshaw wala Kshatriya will take a great deal of pride in their caste, and view themselves above the millionaire Dalit socially. In Muslim society social status is more important because we view ourselves as mixed of all groups who have lived in the subcontinent. No one is impressed by a poor person regardless of what surname they might have.
Anyway the culture that Muslims created, which is practiced no where else but the subcontinent, is equally foreign for many Hindus. With one exception any thing Hindus like is ok. So the clothing, architecture, cuisine, music, poetry, etc, that's fine, however credit does not go to Muslims. Its either shared, a joint venture between foreign Muslims and Hindus, or Hindus must have done it. The idea that the Muslim culture of the subcontinent was created by the Muslims of subcontinent is not acceptable.
However what Hindus don't like or not give importance too such as Nastaliq script, or the amount of Persian/Arabic words in Urdu, giving names is not acceptable. We can look at the Hindi movement, which was done to replace Urdu because it had too many words from Persian and Arabic, and the script was perceived to be "foreign". Shuddh Hindi a language that very few can speak was a result. This would be the equivalent of people wanting to go back to Old English, because modern day English has too many French words. This was started long before BJP came into power. They are simply finishing the job.
The problem is not that Hindus want to do this, the problem is that they also want Muslims to do this. For instance even among the so called liberal Hindus on this forum I have heard why did Pakistan select the foreign Nastaliq script.
The biggest difference between the liberal Hindus and the BJP type ones is the degree which they want to remove Muslim culture. The liberal ones are not interested in renaming cities with Muslim names, or vilifying Muslim rule, however for them its a small part of India's history. And they are willing to throw a few bones to keep Indian Muslims happy. For the right wing type the Muslim era is a dark age, and they need to remove everything from that period.
Their is a small amount of truly liberal people, the aman ki asha bridgade, who don't want religion to divide people and would rather focus on the things that Muslims and Hindus have in common than different. These people have their heart in the right place, but the reality is that in the subcontinent we are divided into ethno-religious groups, and even if religion did not exist we would never have the same history, give importance to the same things, or ever agree on sharing power equally.