What is the view of Buddhism in correcting others' view in spite of their willingness to accept it? I have these questions:


If an enlightened mind sees that helping someone is beneficial to them, then would they do it even when the helped doesn't proactively ask? 
If they are hated by the helped, then would that hate be irrelevant to the intention? Is it perfectly fine to continue the help despite of the rejection? 
How is that different to converting them? 


My self-answer is that of course it is fine to do that, given that the helper is truly sure that their help will bring benefit in the long term. There are many such stories about the ones sacrificing themselves to rescue those who try to kill them, Buddhists or not. However, from the perspective of the receiving end, it is still unsolicited help. They only see that action as unsolicited, or even stalking. They may even see the helper is having a big attachment/mental problem. Although this is just a misunderstanding, I think the helped has the right to challenge that intention.

How does Buddhism address that?



For the question that how the helper knows what is beneficial to the helped, read Does following logic necessarily require one to conclude that they are objective and have no bias?
If an enlightened mind sees that helping someone is beneficial to them, then would they do it even when the helped doesn't proactively
  ask?


Yes. They would help without being asked, as the Buddha did. However, the Buddha did this relatively rarely and only to those he knew he could help. The difficult issue is actually knowing intervening when not asked will benefit the person. For example, often I would like to help some people but sense I cannot actually help them; given they are difficult to change. 


  If the enlightened one is hated by the helped, then would that hate be irrelevant to the intention? Is it perfectly fine to continue the
  help despite of the rejection?


An Enlightened One, that knows the mind of others (due to psychic power) would not try to help another who would reject them. As I said, the difficult issue is truly knowing we can help another. 


  How does that be different to converting them?


The Buddha converted many individuals however only because he knew it was the best thing for them; due to their inherent disposition. As the saying goes: "When the student is ready; the teacher appears".  


  My self-answer is that of course it is fine to do that, given that the helper is truly sure that their help will bring benefit in the
  long term.


Yes. We agree. 


  There are many such stories about the ones sacrificing themselves to rescue those who try to kill them, Buddhists or not.


Angulimala Sutta. 


  However, from the perspective of the receiving end, it is still unsolicited help. They only see that action as unsolicited, or even
  stalking. They may even see the helper is having a big
  attachment/mental problem. Although this is just a misunderstanding, I
  think one has a right to challenge that intention.


Someone who can be helped will be grateful. I think there would be nothing worse than learning that someone who could truly actually help you decided not to help you. It is best to follow the example of the Buddha. While the Buddha did not attempt to help everyone, the Buddha did intervene unsolicited to help those who he was absolutely certain he could help. 

Note: Since we do not have psychic powers, it is rare we can be certain we can help another, unsolicited.