What does it matter if Syndicate members are trusted or rivals with one another?

Can't tell if there's a difference between the two. Each member's reward outcome is already preset by the division of the Syndicate they're in, so what difference do trusted relationships and rivalries do for Syndicate members?

The relations affect how the syndicate events in each area/map playout. Its simpler to explain with an example, (assume Jorgin is not being interrogated and other relations are the same)

If you happen to encounter a fortification event in a map where 'Leo' is the central agent, There is a chance that he will be assisted by any of the agents that trust him (in this case Janus [yikes], Aisling, Riker and Korell) while the rivals (Jorgin) will hinder them.

When receiving assistance they will actually also fight you and you will have more opportunities to affect the syndicate if you beat them before they run away (only happens after you kill the central agent and some time has past)

When being hindered the ones hindering them will fight against the agents and assist you (much like Jun) and disappear after you clear the safehouse (not sure if you can kill them, personally I have not been able to do so). Keep in mind anyone being interrogated cannot help or hinder in any manner

Rivalries are better than Trusted relationships. If you can kill the person assisting you during the conflict, you can rank up either of them. It's better because normally you need 3 people to show up to rank up anyone. With rivalries it can just be two people.