I like to imagine that the Steel Meridian and Perrin Sequence's dislike towards one another... is one sided on SM side.
The PS is established to be pacifists who try to find common ground with literally anyone and anything, whereas Steel Meridian have two reasons to dislike them:
1) Grineer are naturally hostile to all outsiders and Corpus are probably their most "natural enemies".
2) It's a pacifist vs anarchist mindset. I can imagine the Steel Meridian might not like a let's-be-fwiends approach AND might see the Perrin Sequence as paternalistic in how they try to essentially take the disenfranchised under their wing and rule over them via trade/money.
And maybe another thing would be that since Perrin Sequence are friends with New Loka this would also strain relations between PS and SM, as New Loka would object to their allies being allies with someone they view as impure.
But also after the Silver Grove maybe New Loka becomes more "open minded" so a shaky truce can be found between the three. But very slowly and with a lot of setbacks along the way.
Lol this turned into a whole mess of an idea