Most Helpful Girl
There is that possibility that you may be overlooked because of your hair. I know that is unfair, but that is how the working world works, unfortunately. Any business has the right to decide not to hire you. They may have another candidate who they feel suits their 'image' then they may choose to hire another candidate instead. I personally don't agree with it, it should be the person best suited for the job. And if you have a great resume, that should be the focus. But businesses are very concerned with how they are viewed, so that is why you may face some hurdles. And if they hire you, you become a representative of their brand. And Branding is extremely important to companies now a days.
If you have no problem with changing your hair, then that might be an option for you. Some places will hire you regardless, so it isn't impossible to find a job. It just makes it harder.