Also, why does it piss of the TradCaths so much?

but what exactly makes it so controversial that someone goes out and kills a priest over it?

Rich people, specially in LATAM, hates being told that they are wrong. Also, the US and Salvadoran goverment saw him as threat, because he was advocating for peace, and they knew that if there was a fair election, the communists/leftists would win.