Can I dye my hair an unnatural, out there color without it hindering my ability to get a job?

You already have to know that yes, it will make a difference. Unfortunately, the first thing we are judged on is are appearance. Of course it depends on the type of job you are applying for. While working in a tattoo parlor it would likely have no bearing whatsoever, but in 'corporate america' you have to be able to conform to the status quo. Maybe you could find something non permanent for the weekends that you could wash out during the week?