Do the Indians of today still consider the Mughals as invaders?

I believe I have enough knowledge of Mughal history and India's social dynamics to answer this question.

Do the Indians today still consider the Mughals as invaders?

The answer to this question depends on your politics more than anything else. Hindu nationalists, a fundamentalist fringe in Indian politics, do consider Mughals and all other Muslim rulers as invaders or colonisers. They make sure to mention at every turn that India has been colonised for 750 years and not just the 200 years during the British Raj.

The above people however are still a fringe population (albeit with considerable political power) in India. Most ordinary people, not too well-versed in history, don't consider all Mughals to be the same. A lot of conservative Hindus don't have much love for the Mughal emperors and assign a lot of blame for India's problems on them (most of them incorrect), but don't consider them invaders or outsiders. A glaring exception is Akbar. Even conservative Hindus rarely question Akbar's integrity or his commitment to his people.

The traditional and the most common opinion though goes something like this. Babur, the founder, was an invader and hated India (which is true, even the hatred part). His son, Humayun, was a meek scholar and an ineffective king who first lost the empire for about 15 years before regaining it and then died by falling off the stairs in his library (very unlike a true warrior's death). His son Akbar was crowned the king at 13 and was the best thing to happen to medieval India.

Indian pop culture, folklore and urban legends are full of stories of Akbar's wisdom, sense of justice and fairness and religious and cultural tolerance. Plenty of people like the retired Chief Justice of the Supreme Court of India, Katju, consider Akbar to be the founder of modern India. Much of modern Indian society's interpretation of secularism, pluralism and multiculturalism is based on Akbar's laws and decrees.

Akbar's cultural reputation in India as epitomising the values of tolerance and pluralism while staying unambiguously ambitious in empire-building is hard to overstate. This is not undeserved either. Akbar's half-century reign established a legacy in India that was impressed in people's minds for centuries afterwards. Later political powers like the Sikhs, the Marathas and finally the British had to pretend to rule as the proxies of the then-weakened Mughals because people everywhere, Hindus, Muslims and others, still considered Mughals as the true rulers. The Revolt of 1857 was led by Maratha kings and generals and yet, the revolting soldiers of the British army wanted to re-establish a Mughal empire, going as far as asking the last Mughal to lend symbolic support.

Back to people's perceptions. Akbar's son Jehangir is known as the indulgent king who listened to his beautiful and shrewd wife more than he should have (mostly misogynist reasoning; his wife didn't cause any grief to the empire or the people). Jehangir's son Shah Jahan was a connoisseur of the arts and architecture and built the Taj Mahal and was again, too soft and indulgent.

Shah Jahan's youngest son, Aurangzeb, who murdered his brothers and imprisoned his father to ascend the throne, is considered the most evil. A British-era road in Delhi named after Aurangzeb was recently renamed and most people couldn't be happier that such a fundamentalist Muslim king doesn't have his name immortalized on Delhi's roads. Aurangzeb's legacy might have been more nuanced but his fundamentalism and orthodoxy is what people in India, Hindus and Muslims alike, remember him for.

The emperors who came after Aurangzeb were presiding over a crumbling empire as proxies of the Sikhs, Marathas and finally the British. Most people don't know their names.