There was not a war because of it. There was a war for territory between the Federation and Cardassians which somehow never managed to involve Bajor at all, despite the Bajoran exiles begging for Federation interference.
We just don't know exactly. What we know is that the Cardassians were expansionist and invading other species, and that the Federation were at war with them.
What we DO know is also this: One of the corner stones of the peace treaty (with a lot of diplomatic soft power by the Federation) was that the Cardassians stopped their occupation of Bajor. Suggesting
again that the non-interference clause is something at least the Federation forces upon others.
No one disputed the Vulcans. And ALL of the sample size of Klingons and Romulans has practically nothing to do with this question. 99% of Klingon and Romulan appearances don't involve third party races AT ALL. Almost all the remaining examples involve third parties who are caught between the Klingons/Romulans and the Federation, which do not tell us anything about the normal operations of the Klingons or Romulans.
How many examples can you even name of the Klingons or Romulans having any relationship at all with a minor planet outside of the handful of worlds the Klingons and Feds were fighting over in TOS? You can't make a judgement about how someone treats other people if you never see that person with other people.
Considering the Romulans and Klingons all have warp drive, they would have access to
all those pre-warp planets the various Enterprises visited. And they were
never contaminated by them. Not once! After such a big sample size of untouched civilisations (and NEVER a contamination without diplomatic consequences like war) it's pretty obvious that all those other species don't really mess with pre-warp civilisations either. And I just don't believe they do it because of good-will.
This seems like the space UN doesn't allow for species to invade other species, mess in their internal affairs, or generally make contact with pre-warp civilisations.
Some bad guys don't like that and often break that rule (klingons secretly messing with pre-warp civilisations, Cardassians occupying other species, Russians invading Ukraine), which has diplomatic consequences (war, sanctions, whatever), but also has the side effect that the
good guys also aren't allowed to interfere, even though it would be the only way to help those people from extinction.