Do I need to learn Hadoop to be a Data Scientist?
Different people use different tools for different things.  Terms like Data Science are generic for a reason.  A data scientist could spend an entire career without having to learn a particular tool like hadoop.  Hadoop is widely used, but it is not the only platform that is capable of managing and manipulating data, even large scale data.

I would say that a data scientist should be familiar with concepts like MapReduce, distributed systems, distributed file systems, and the like, but I wouldn't judge someone for not knowing about such things.  

It's a big field.  There is a sea of knowledge and most people are capable of learning and being an expert in a single drop.  The key to being a scientist is having the desire to learn and the motivation to know that which you don't already know.

As an example:  I could hand the right person a hundred structured CSV files containing information about classroom performance in one particular class over a decade.  A data scientist would be able to spend a year gleaning insights from the data without ever needing to spread computation across multiple machines.  You could apply machine learning algorithms, analyze it using visualizations, combine it with external data about the region, ethnic makeup, changes to environment over time, political information, weather patterns, etc.  All of that would be "data science" in my opinion.  It might take something like hadoop to test and apply anything you learned to data comprising an entire country of students rather than just a classroom, but that final step doesn't necessarily make someone a data scientist.  And not taking that final step doesn't necessarily disqualify someone from being a data scientist.