If a women chooses to wear it than no one can take that away from her. Someone forcing her not to wear it when she wants to is just as bad as someone forcing her to wear it when she doesn't want to. It's the woman's choice not anyone else's.
I believe that a woman has a right to wear whatever garment she wants and I especially feel this way if it expresses their religion. No person, group, organization, or government has a right to tell people what they can or can not wear. It is important that a person feel they can express themselves whether it is religiously or politically, or however they want.
Now under the assumption that you meant a verbal fight, an intellectual war of words, then yes, you bet it is worth fighting for.
This is Islaam. Qur'an, Sunnah, Salaf and the Scholars.
First you have the word of God, then you have the teachings of the prophet Muhammad, then you have the understanding and interpretations of the Companions, then you have the interpretations of the rest of the Salaf, the first three generations of Muslims, and lastly you have the interpretations of learned Scholars.
Every last one is clear in that the hijab is obligatory. To deny this is a form of kufr, disbelief. There is no going around it, there is no taking it out of Islaam. Unless you're not Muslim, like the Qur'anists, or some other heretic.
If you meant a physical fight? Then no. Of course not.
When there are cultural norms there are almost always disagreements between groups that do not share the same norms. The hijab is worth a discussion and debate but nothing more, it is not worth physically fighting over. With the fleeting nature of societal norms it should be understood that opinions and practiced cultural norms change over the course of time and should not be considered blasphemous when not strictly followed.
Why would anyone want to fight over a hijab? The hijab is a sign of modesty. I think it is a major sign of respect for women to wear it. It shows she has respect for her body and donesnt share it with anyone but her husband. However, many see the hijab as a sign for men to keep women silent. Most women are stereotyped when they wear the garb, especially since 9/11.