Muslim here. No there is no prohibition against dogs in Islam, but more of a taboo surrounding them which goes back to some specific events in our early history (you can look this up).
Regardless, by no means was the taxi driver entitled to refuse the disabled individual and their dog. This isn't a question of religious liberty, but civil rights. The taxi driver couldn't and shouldn't be able to refuse providing his service to a black man simply because he's black, because he's discriminating against him on the basis of something he can't control. In the same way, the disabled person can't control their condition, and to refuse a service to them on the basis of it is a breach of his/her basic human rights.
And anyway, discriminating against such a vulnerable person because of a taboo is both dumb and disgusting af.