Learn Russian: Агрессия по отношению к коллегам ломает доверие. - Aggression towards colleagues breaks trust.

Yes, you could, but по отношению к (literally "by relation to") is much better suited for describing professional, social, or psychological stances. It sounds more formal and precise than just к (towards), emphasizing the nature of the behavior directed at the colleagues. Both phrases require the target to be in the Dative case.

Which part of по отношению к forces коллегам into the Dative case?

It is the final part, к. The compound preposition is made up of по + Dative (отношению) + к + Dative (коллегам). Whenever you use к to mean "towards," the target of that direction or attitude must take the Dative case.

Is ломать доверие a literal translation of "to break trust", and does it sound natural in Russian?

It is a literal translation, and it sounds perfectly natural! Just like in English, you can physically break an object (ломать стул) or metaphorically break trust (ломать доверие). In very formal business contexts, you might also hear подрывать доверие (to undermine trust) or разрушать доверие (to destroy trust).

Why doesn't the ending of доверие change if it's the direct object of the sentence?