Well, of course not. Generally speaking, hair dye cannot lead to vision loss in your eyes, so you do not need to worry about it. In common, as we know that hair dye is made from chemical material. And this chemical material can just be irritants in the eyes. So if you have got hair dye into your eyes, just try some ways to get it out, or it can just infect your eyes, leading to some eye infection. In my opinion, you should wash your eyes with pure water as soon as possible, so that it can just wash hair dye out. Also, having some eye drops, and cold compresses can be beneficial. Anyway, just be careful.
It is true that hair dye products is highly irritate, which could have some very dangerous effects on your eyes, even make you go blind. So, for this moment, you need to use plenty of normal saline to flush your eyes, then go directly to an eye clinic for professional and timely treatment, come on. Time is of the essence!! Remember, do not try to rub your eyes, that is deadly.