Monster unaffected by Spell/Trap vs. Monster given protection via Spell/Trap
The thing here is that the one unaffected by spell/traps is your monster.

However, that does not make your opponent's monster unaffected by spell/traps.

Protecting your monster from spell/traps does not negate a spell/trap card that affects your opponent's monster.

You could, however, make your opponent's monster unaffected by spell/traps (for example targeting with whatever effect made your monster spell/trap proof), and if you do that then the spell protecting it from being destroyed won't save it from your attacks.