Are stores and restaurants closed in Spain on May 1 for International Workers Day?

Being the original poster I thought I would provide some new info for those who read this: I asked a host at my hotel in Bayonne, he said here in (at least this part of) France that ‘everything will be closed, even the buses’, but restaurants will be open. And he further said that in Spain it is ‘not the same thing’ and that places are more likely to be open on May 1 in Spain than in France so it may be a good day for a day trip to San Sebastián by train.

Here in Barcelona, we expect a lot to be closed - for example, El Corte Ingles is closed across the city - but you may be luckier with restaurants, as the ones that are open do brisk business on holiday-closure dates. If there's anywhere you particularly hope to eat or shop, I'd give them a call just to check - but know that there will definitely be some bars and restaurants that are open, because we all have to eat somewhere!

Most shops, supermarkets, banks...will be closed. There´s no reason at all for bars and restaurants closing, it´s a great day for them, lots of people will eat out. Donostia-San Sebastian will be packed, manage your itinerary wisely!

Thanks for input
I got to Donasto-San Sebastián by regional train using Bask Pass from Bayonne (only €14.30 round trip!). I walked along beach and past the boa’s to the Basque Naval Museum )Euskal Istas Museoa). I expensive and very well done exhibit on Basque involvement in Maritime law and trade. English language panels
provided for each item. Once I was ready for
lunch I picked a place that was not open just yet and stood in a line at La Cuchara de San Telmo near the San Telmo Miseo. So yummy! then I ambled around a bunch more in the less touristy streets my way back to the train station. A good May Day spent. (hmmm this is sounding like a trip report now)

May day is past, but we were going from Madrid to Seville on May 1st, some observations in case anyone finds this in a search...

Make your train plans well ahead, they are running, but all the trains headed to Seville and the South anyway, were packed, as was the train station. Some was likely due to May 1 falling on a Thursday, and Madrid celebrates May 2 as a holiday, so many were off on a 4 day weekend. Ticket prices were also higher.

Most (not all) restaurants and bars will be open, public transport is running, but most shops, grocery stores, and businesses will be closed. Tourist oriented shops though might be open, and for some reason many shoe stores were open, just sort of random what was open. Tourist sights all seemed to be open.