DISCLAIMER: THIS POST WILL NOT TEACH YOU EVERYTHING YOU NEED TO KNOW ABOUT THE SPANISH CIVIL WAR, OR EVEN ABOUT ITS MUSIC.
Well, one famous thing about the Spanish Civil War is the International Brigades: volunteers, largely in highly varied shades of leftism, from all over Europe and the world who showed up to fight the fascists. (Anglophone readers may recall Hemingway's For Whom the Bell Tolls and Orwell's Homage to Catalonia.) So alongside the songs in Spanish and Catalan that came out of or get associated with the war, there are many International Brigades songs in English, German (yes, lots of German communists and other anti-fascists in the '30s went off to fight fascism where it seemed vulnerable), Italian (ditto), French, and this collection appears to have at least one each in Czech, Polish, Hungarian, and one that's attributed to "Yugoslavia" but I do not have the South Slavic expertise to tell you what language it is in. Not a song, but I have seen a poster specifically recruiting Esperantist volunteers. Very multilingual environment already.
And then... the Spanish Republic lost. The fascists won. The songs went pretty quiet in Spain. But the international volunteers that survived and went home kept singing them. And so did one of their sympathizers: Pete Seeger, whose recording Songs of the Lincoln Brigade introduced many of them to a broader audience. On that album you can hear Seeger singing songs in both English and Spanish:
Or how about the German communist volunteer and singer Ernst Busch doing the "Song of the United Front" in Spanish, English, French, and German:
(oh gosh my YouTube music recommendations are going to be so communist for a bit. That's all right, they've been quite Jacobite lately so that will balance it out.)
Of course, fascism in Spain didn't last forever, and today many singers and groups in Spain do perform and record the same songs. ... Including the International Brigade ones. (Unfortunately I can't track it down, so this may not be true to any extent at all, but I have read a remark somewhere [possibly in someone's liner notes?] that after the death of Franco, young people in Spain rediscovered these songs specifically through Pete Seeger's recordings...!)
So you can find the Catalan "Quartet Brossa" singing the Italian Bella Ciao:
Or the evidently Spanish-speaking "Coro Popular Jabalón" doing their best American English in the soldiers-complaint song "Quartermaster Store":
On the same album they have a song in Basque:
(You may have noticed Spain's minority languages, including Catalan and Basque, making a good showing here: that's no accident, those were evidently quite republican areas, as will not surprise you if you know anything about Franco's language policy.)
Anyway those are the main historical reasons I'm aware of why music from and about Spanish Civil War is so multilingual. Obviously my original claim that "almost nobody is ever singing in their native language" had an element of hyperbole - the Americans do sing songs in English (as do the Irish), the Spanish in Spanish, the Germans in German, and of course the Catalans in Catalan. But if you look for Spanish Civil War music, many of the "standards" you'll find are International Brigades songs, many others are Catalan as well as Spanish, so no matter what your native language is you will have plenty of songs that aren't in it.
And apparently you sing them anyway. Because, at least for the people making these records, it seems it's not about where you're from, or even whether your accent is any good, it's about standing side by side.
And that's why I said it's beautiful.