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Interesting question. I don't have a dog so it had never crossed my mind. I've just done a bit of Googling and, generally, it seems to be up to the individual drivers and taxi companies. I did find at least one place that had a scale of fares for dogs, though I can't find it again, there were stories about dogs being allowed onto buses and taxis in Aragon as well as some places where it was  not permitted. Guide dogs have no prohibitions of course.

I live near Benidorm and they definitely do not allow dogs in taxis here or on buses. Trains allow them if there in a pet carrier and weight about 6 kilos. On autobuses they have to be in a carrier and they are stowed away with the luggage

As so many Spanish people here in El Campello have dogs and are evidently enjoying the love of these domesticated loyal animals then why are there no dog friendly taxi drivers, hotels or hostels.we have a beautiful dog park and beach and it's great to see owners and dogs enjoying these benifits.  We have three little dogs and the only place we can travel to each summer is Bilbao where we atay in a lovely clean and well cared for hostel. The kind owner even pet sits while we go out. Taking care of dogs on holidays could be a very lucritive business for any budding entrepreneurs  out there  as there are so few trustworthy dog kennels around. We visited a few without appointments and we' wouldn't leave a cockroch in some of them.
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I caught a taxi in Javea and was allowed to have my dog, a staffie cross, in the back with me providing she sat in the foot well and not the seat. Driver discretion, I guess.