That depends on three things; that is, how do you define:
1. Independent (political, thought, culture, religion. etc.)
2. Morals (What particular morals are you referring to? Morals that are acceptable in one part of the world / culture may not be acceptable in another)
3. Strength / Weakness (What some people may see as strength (e.g. a willingness to compromise for the greater good, may be seen by others as weakness.)
From a personal perspective, I consider myself to be an 'independent' person - I don't follow many cultural norms (I'm vegetarian, Spiritual rather than religious, Liberal in my political views, Eccentric (British), have decided not to have children and enjoy pastimes others may not consider to be 'ordinary'.)
As to whether I am morally stong or weak, I think it's extremely important for me personally to have a moral code, which for me means the following:
- Taking responsibility for my actions
- Being kind to others
- Communicating honestly and with truthfulness
- Keeping an open mind
- Understanding when I am wrong
- Having a 'live and let live' attitude (i.e. everyone is entitled to think and believe what they want to)
I'm not sure if that make me strong or weak - All I can say is that I continually test my moral framework over time and if something isn't working out for me, try to define why and how to rectify it.
I realise this is a very subjective, personal answer, but I can't be more specific unless I understand the framework you are posing the question under.