What might be considered intrusive in many Western cultures is only a matter of course in India. Also, people will generally be very curious about foreign visitors, and this can take the form of unabashed staring.
There’s a lack of privacy among the teeming millions of India, and the concept of personal space as you know it might not exist.
Try not to take it too personally if people on the street seem to be staring at you all the time, and if Indian acquaintances and friends ask you questions that you think are none of their business.
Most of the time, it’s just friendly curiosity, and if you smile at a staring stranger, many times you will get an amicable smile back. However, never sacrifice safety for the sake of politeness. This is especially true for women travelers.