Finished the last bit of the Camino Portuguese at the beginning of October. Thoroughly enjoyed the experience. Gave up alcohol over two years ago so I stuck to Estrella Galicia 0,0 (zah-roh, zah-roh, as I learned). Lovely alcohol free beer and, as you say, always with a tapas!
I can't speak for Spain, but in Portugal, there seems to be widespread local acceptance that the traditional casual approach to alcohol consumption (perhaps just a North American cliche of European life) isn't for everyone. Coming from Canada, I was surprised and pleased to see that all of the major brewers produce alcohol-free versions that are marketed right along-side, and equally "seriously" as, alcoholic beer. They're sold side by side in the supermarkets, and both are advertised equally, on the same page in the same section, in weekly sales flyers. It seems quite matter-of-fact that someone might want either.
The phrase"sem álcool," shown on flyers/labels as "s/álcool," means "without alcohol," and that's what you'd ask or look for.
Non-alcoholic wine not so much, because the locals are so proud of the various regions' wines and they get a lot of publicity as national and regional products, just like cheese! But nonalcoholic wine is present, as well, and where you find it, quite drinkable.
Also, I was surprised, given my beliefs about the culture of Iberia, to find that a significant number of my neighbours in rural Portugal actually didn't drink. The accepted reality is that alcohol is everywhere. Not the case!
**Later edit: the above is definitely not true for coffee, however...it
is everywhere!