One of the things I love most about The Smiths is the pairing of Morrissey's morbid sensibilities with Johnny Marr's jangly, upbeat riffs. Here are some songs with similar contrasts.

Maritime: Someone Has to Die
Malthusian logic at its most musical.
https://www.youtube.com/watch?v=Rh3y-rJgkuc

Chumbawamba: El Fusilado
Would "Tubthumping" have been such a huge hit if people realized Chumbawamba were an anarcho-socialist protest band? In any case, this is the catchiest song about being at the wrong end of a firing squad I've ever heard.
https://www.youtube.com/watch?v=MWT6994z7cE

Math & Physics Club: Will You Still Love Me
Sucks to get old.
https://www.youtube.com/watch?v=svVUeu96SCg

Strawberry Switchblade: Since Yesterday
If not for its classical underpinings, this pop confection might be forgetable. Wait, what are they singing about? A breakup or a suicide pact? (If that's not enough, there's a less famous song where Rose McDowall's elfin voice promises "I will take you by the hand . . . and I will cut you with the cake knife.")
https://www.youtube.com/watch?v=B0bnypWItlY

Club 8: We're All Going to Die
Yes, that's true of course, but I still did a double take when my sweet Swedish background music turned nihilistic.
https://www.youtube.com/watch?v=04x7LVssoow