I had conversations with two dog-accompanied pilgrims on this on my last two Caminos. A German teacher told me that he decided that he would just take hotel rooms in places which accepted dogs; his Spanish was fairly good for calling ahead and booking, and by Triacastela, he had encountered no problem. I had dinner with him at three places and, in all of them, waiters brought out bones for the dog's dinner. The other was a Slovenian woman who slept outside albergues with the dog and her friend-- none of them would admit the dog to the dormitories and she never asked that they do so-- she told me that she knew that many people were very uncomfortable with dogs. On a few occasions, the hospitaleros let them sleep in an outbuilding. I would note that, in both circumstances, the dogs were very well-behaved and affectionate-- the Slovenian dog was of such a disposition that he made friends with the most vicious-looking guard dogs and mutts along the way--- I have never seen anything like it.
While I am not a fan of taking dogs on the Camino (my fuller opinions on this are available on other threads), it seems that it can be done provided you are willing to: a) get a hotel room or b) sleep outside. In the case of a), you would be advised to learn a few basic sentences in Spanish to make clear to innkeepers what you are requesting and, if they are not receptive, to ask them to recommend somewhere else in the pueblo. I have found that turismos are very happy to be of help (well, not in Santander, where I found them a bit grumpy). As well, I have a vague memory that there is an English dog-owning tourist guide to beast-friendly accommodation--- a quick google did not find it, but perhaps other forum members may be aware of it.
