It's not "Indians" that are pushy.
Not "Indians". That makes it sound like everybody. It's "rickshaw drivers, taxi drivers, and some street vendors in India."
I never found pushiness from regular people other than when queueing up to buy tickets at the train station. Just from people in certain professions, and mostly in touristy areas.
So it's not really based on race or nationality, but on profession and opportunity.
Yes. It's definitely worse for foreigners / westerners / "white" people, but ...
You can actually chat to these people. I try to keep a good sense of humour and ask them if they hassle Indians as much and they tell me no because the Indians don't like to pay them much money. They really like it when you treat them like real people rather than just annoyances. It might not make them leave you alone but it leaves you both happier being friendly with them than being adversarial.
How to avoid a lot of pushy drivers and vendors.
Keep away from the busiest tourist zones when you can be somewhere else. Sometimes you can't avoid it, like exiting a train station, or arriving or departing from a tourist site.
But other times, such as getting things done in a city like Mumbai (finding a restaurant, buying supplies, getting the feel of a place) all you have to do is take some road other than the main tourist road. In Mumbai the next street over from the main tourist street I found everybody so nice, nobody pushy at all. The pushy types follow the biggest chances of money.
Even if you're in a busy touristy place and you want something, avoid the loud drivers and vendors. They are good at getting people's' attention and then getting their money. But there are also plenty of meek people in India who can't bring themselves to act like this. They might have the next fruit stand over from the loud pushy guy. They might be waiting patiently in their rickshaw elsewhere in the train station grounds rather than crowding around the exit doors. Go to those quiet people instead. The noisy ones see that they've lost you as a potential customer and look for somebody else to annoy.
When regular people are pushy.
As I mentioned the one place I found non drivers non vendors to be pushy is when queueing to buy train tickets at stations. Toward the end of my month in India I finally learned the trick for this. Be nice and happy and smiley and friendly and say "namaste" to people.
It was amazing. People suddenly saw me as somebody like them rather than as an ignorant outsider tourist. They filled out my forms for me, they pushed other Indians out of the way to get my form to the ticket seller behind the window!
India has a different flow, you have to learn how to go with it.
Just because of its unique properties, like the huge population, the huge gap between rich and poor, the poverty of the poor, the crowding, etc, it's not like most places you might travel.
For this reason the ways you normally go about things can cause some friction that will make you grumpy and tired.
Getting grumpy and tired isn't nice. The best thing to do is to take the opportunity to learn about people and learn about yourself by thinking of new ways to do things that are different to how you would normally behave elsewhere, but work smoother in India and leave you less grumpy and tired.
It's not easy, especially when you first arrive, especially if it's hot and humid. But when you finally "get it", it's really rewarding and you will fall in love with India!