refillable water bottles in Barcelona museums

I don't know about Barcelona, but in France and Italy we carried our Contigo water bottle all over, including inside museums and all attractions. Thank god we had it, we filled it with ice and water every morning and had ice cold water all day, and refilled at water fountains in Italy. We have some cool dings on the container from falling inside the catacombs in Paris and the streets of Italy, each ding means something to us!

I had mine everywhere in Barcelona and was never stopped. I carry a messenger bag and the bottle was closed and visible in a side pocket - obviously don't drink from it inside a museum! I would leave it in the bag, and if you are concerned empty it before going in. They won't ban you from having an empty bottle in your bag, although I suppose I could see a problem with a full bottle as a spill could damage something. Never had anyone give me any trouble, though

Reduce - Reuse - Recycle
is not a new, or American, idea, you know.
They've been husbanding their resources so that they go far in Europe since Homer was in short pants.

More specifically, I have carried a water bottle into many museums in Barcelona with no ill effects. I keep it in my RS civita shoulder bag.

Museums usually have handy, free cloakrooms/bag storage, where you can leave a bag that is made heavy by water bottle or any item that staff tell you not to bring in. Drinking fountains are not as common in European public buildings as they are here, but you may find some in museums.