Is travel in Spain unusually difficult or inconvenient on May 1st, compared to other days? It's International Workers Day; I have this feeling it may be a crap shoot in terms of demonstrations and strikes affecting air and train travel, which would make it a bad day to arrive.
I think there is some kind of confusion here: on May 1st there are indeed demonstrations, but like in any place where unions are present and want to celebrate their day / the labour day.
Strikes are not scheduled: there is no special reason why that specific day there will be one. So I don't see any kind of relationship between being 1st of May and having to deal with a strike.
That day is like a Sunday in many senses, where the frequency on public transport is lower and shops are closed. Apart from that, everything should be normal transport-wise.