There's a number of verses in the New Testament which arguably instruct people not to swear. Colossians 3:8 is probably most on point, although as with all cross-cultural comparisons of foul language, it's hard to know exactly what a Greek speaker 2000 years ago would have understood αἰσχρολογία to mean in the context of modern English.

Many religious texts have broader restrictions on word usage than just their deity's name in vain. Usually those are adjacent to other aspects of the religion. I am not aware of any that would forbid what we would commonly call swear words.

It's the same motivation as racists: they need some way to feel superior to the people that they despise. If the entire world stopped swearing today, these people would just find something else to use in their supremacist proxy wars.