What do you call a person that is consistent in her beliefs despite the difficulties they might cause?

I am sure there has to be a more precise word to describe a person that is not giving up on her beliefs no matter what other says. You could say consistent in her beliefs, but I am looking for something more elaborate.

An example of such a person might be Margaret Thatcher.

Thanks

"...no matter what others say." Are the "others" right and that person is stubborn, as @Charon offered, or are they "resolute"?

Resolute as defined by the FreeDictionary.com:

Firm or determined; unwavering.

steadfast seems to satisfy your requirements:

unwavering, as resolution, faith, adherence, etc.

Google defines it as "resolutely or dutifully firm and unwavering," so, if you like resolute, then you might like this, too.

How about stubborn?

having or showing dogged determination not to change one's attitude or position on something, especially in spite of good reasons to do so.

"you're a silly, stubborn old woman"

_OED

Your question reminded me of this passage from Profiles in Courage by JFK, and depending on context, I would say the person is "courageous".

It takes great courage to do what you think is right even though it may mean the end of your career and the dislike and criticism of your friends and neighbors. Many people never have the opportunity to show such courage. But all of us have the opportunity to recognize such courage in others, to respect the person who is doing what he believes to be right even though we think he is wrong......Courage is much more than bravery on a battlefield; it can mean acting according to your beliefs whatever the consequences......We can all share in such courage by refusing to join with those people who make unreasoning attacks on the man who is doing or saying what he honestly believes to be right.

John Fitzgerald Kennedy, Profiles in Courage, Harper & Brothers, New York, 1955.

I think that adjective fits Baroness Thatcher perfectly.