Monica put yourself in the man's shoes rather than the woman's shoes, from the nature of your questions I think this is where your confusion stems from. Since you can personally relate to the woman's condition, you must be careful not to bias your judgement.
Christianity, when practiced properly, is a pretty tolerant religion so it is hard for me to make a direct analogy. So for a moment imagine that somewhere in the Bible God has declared that dogs are unclean creatures, and contact with a dog makes a man unclean. This carried various consequences that usually included inability to participate in society until certain periods of time had passed and certain sacrifices had been made. To give an example of God's treatment of unclean entities, consider Leviticus 12.
After giving birth, a pregnant woman must avoid anything sacred for a period of up to two weeks and 66 days depending on the sex of the child. After this, she must bring animals to the priests for offerings to remove her unclean status. Obviously this shows that being unclean causes places pretty severe restrictions and responsibilities upon an individual.
I cannot speak with authority on the practices of Muslims with regard to contact with dogs, but I can assume that since God's laws seem pretty harsh Allah's laws will be likewise.
Furthermore, cab services are typically not entities of the state nor are they public transportation, meaning they have the right to discriminate among their customers as they wish. There would still be outcry had the man refused services to a Jew, but if the Muslim faith held Jews to be unclean I would still believe he was not acting wrongly.
All things aside, there is a single action the man could have done that I think would have reduced the fallout here: call for another cab. This simple act would show that while he could not offer his services for religious obligations, he was sensitive enough to the woman's condition to still assist her.
Basically, I believe to charge the man with discrimination you must first prove with reasonable evidence that Islam is a false religion. I can no more prove that Islam is false than I can prove that Christianity is true; it is a fallacy to attempt to use logic on issues of faith. If we cannot prove that Islam is a false religion, we must support the idea that if his religious convictions restrict his contact with dogs then he acted with no regard to the woman's disability. If the woman's disability was not part of his decision to reject the dog, we can say that she was not discriminated against.
It is a very tricky issue though, the kind of thing that is fun to think about from different angles.
*EDIT UPDATE*
Oh in light of MacWeirdo's point my opinion has reversed. If the man was legally required to carry guide dogs, then he only has three courses of action:
- Join with like-minded individuals in an attempt to have the law changed
- Get a job that does not leave him legally obligated to participate in activities he is religiously obligated to avoid.
- Live in a place where laws follow a more traditional Muslim life.
Some people would question my law over religion stance, but I strongly believe that in a society that allows citizens to shape the law, the law will be shaped by the cultures within the society. Thus, without law religion is threatened and law is shaped by religion. They are interconnected.
His religion-based refusal is valid but now ethically wrong since it defies the laws of the society in which he lives.