You do not need permission from the individual users.
If you, as a Twitter user, can see a person's tweets then you can see their user information.
Question
Is it possible to access Twitter account information without their consent through API?
For example, if i have an app that is authorized by a single person (if their account is private); and I obtain a list of their followers.
Now, if i need to go through the tweets of their followers; do i need to get permission from each of their followers or should I be able to consume their tweets (if they are public of course) without any permission issue?
Solution
You do not need permission from the individual users.
If you, as a Twitter user, can see a person's tweets then you can see their user information.