I am Muslim, and I walked the Camino this summer. I usually wear hijab in my daily life, but found my normal fashion was not practical for the physical rigor of the Camino. I still covered my head with kerchiefs and moisture-wicking Buffs, and always made sure I had a lightwieght rectangular scarf to wear when in any church -- hey, a house of God is a house of God, right? (Plus, that lightweight scarf doubled as a pillowcase most nights!) Truth -- if you're walking in the summer, you're going to want to cover your head, anyway, to protect yourself from the blazing sun!
Outwardly, I suppose, it wasn't immediately obvious that I was Muslim. But, of course, the topic of faith does come up on the Camino. And the Spanish people, for some reason, are always really curious to know what a person's religion is. At first, I was nervous, but I was always honest about my faith. And I never had a bad experience. A lot of people were curious, and many wanted to know why I was making the pilgrimage. "Don't you have one of your own, to Mecca?" was a really common question. More often then not, I found people to be curious but respectful, and I had many a deep conversation about faith and spirituality along the Way.
Also, I must add, I found many people along the Way to be incredibly good "Muslims" -- meaning, quite literally, people who are open to and accepting of the will of God. And in practice, I found most pilgrims, regardless of religion (even those without a particular religion, too!) to be doing what every Muslim (and Christian, etc.) is asked to do -- welcome the stranger, give to the needy, share what you have, and so on. I like to think it made me a better Muslim.
Look, there are people of every creed, and even a lot of people with no particular religion or faith along the Way. Of course you may meet a few people with unpleasant reactions, but overall, pilgrims are kind and welcoming folk. Buen Camino!