But it would *only* have lead to civil war amongst the Vau N’akat if the Federation had offered them membership and half wanted to join and half did not. Just ‘seeing’ the Federation would not cause a civil war, there has never been an example of this in Star Trek before with other species. Prometheus class ships are beautiful ships though so I could imagine some of the Vau N’akat being jealous and wanting one for themselves and fighting over it. The Vau N’akat is a warp capable species therefore First Contact could have been initiated as per that protocol, but I am sure that the Federation would not have offered the Vau N’akat membership if there were any signs of internal political turmoil as this *could* potentially cause a civil war. This is why it was so hard for the Bajorans to gain entry in to the Federation after the Cardassian occupation and Dominion war. The Bajorans needed to prove themselves to the rest of the Federation and meet a certain standard.
The Bajorans were also all the better for it.
They had to go through a period of recovery/rebuilding in order to get themselves on track... otherwise, the UFP would have been setting a wrong precedent had they accepted Bajor right off the bat.
However, they DID send a contingent of SF officers to DS9 to be there in an admin fashion (and UFP DID send Bajor an industrial grade replicator to help them recover) - which would prevent the Cardassians from reconquering the Bajorans. What Bajor effectively did was driven off the occupational force, but the Cardassians had intentions of coming back to 'finish the job'. The UFP had a small window of opportunity to prevent that from happening, but they also couldn't openly just accept Bajor into UFP. So the next best thing was to establish a SF presence on DS9 and that's what protected Bajor and gave it ability to become independent and mature enough to eventually be offered membership into the Federation.
Obviously, the UFP DID 'interfere' here, but only in the case of preventing an outside force (the Cardassians) from possibly exterminating Bajorans out of existence, and I suppose in this particular case they were not directly interfering in the 'natural course of evolution of Bajor', but rather setting it back on track (by removing the cardassians from the equation).
In the case of the Vau'N'AKat, their conflict was internal... but the Diviner indicates that FC with UFP (a Prometheus class statship) caused a split on Solum... which is possible.
We've seen on other Trek shows that learning of existence of aliens can easily have a polarizing effect on society and cause internal problems because the species is forced to reconcile with the fact they aren't alone in the universe.
In the case of Vau'N'AKat, we don't know if they already were aware of other alien species in the Galaxy... but the way Prodigy told the story, it didn't seem like it.
They seemed to have been advanced enough to have Warp drive and other technology, but they appeared to be in a fairly secluded bit of the Delta Quadrant where not that many alien species might have been around... or the half of Solum which was against UFP in general was anti-alien life in general (the Diviner did describe them as 'weak' etc. - there's a sense of superiority here that is difficult to get by... the 'Order' in particular sees SF and UFP as 'less than').
The UFP couldn't interfere in what was clear an internal conflict. They also didn't do that in the case of Bajor during DS9 run (Bajor had a few internal issues to work out during the recovery period, but ultimately the UFP couldn't have interfered into those internal affairs - SF did deal with threats that were targeted directly at them, and exposed conspiracies and gave it to the Bajorans to deal with the situation as they saw fit).
Solum wasn't occupied by an external force, so SF had no need to leave a contingent there to help them recover from the occupation... Solum was in effect a victim of its own indigenous people.
As for whether some who were pro-UFP turned bad... those seemed to belong to 'The Order'. In probability not all who liked UFP started hating it for not taking sides or helping them, but I would say the 100 people who were part of The Order did and turned extreme (otherwise, the entirety of Solum would have been said to have turned against UFP - but it seems like a small radical group which survived Solum's conflict developed a bad perception of UFP due to their non-interference protocols and ended up becoming extremists who want to destroy SF and prevent FC from happening)... the Vindicator and Diviner being 2 of those 100 - the other 98 either didn't make it through the wormhole and died along with their ships, or they were scattered in different time periods with heavy damage to their ships and are no real threat to anyone (perhaps).... who knows.
I'm hoping the crew of the Prometheus class starship did manage to explain the principles behind the P.D. and why SF can't interfere into planetary internal affairs... or at least they would have, but bitter individuals just didn't care (and we've seen how people who are emotionally compromised can ignore those rules).
What morale guidelines or compasses would be used to decide which side in an internal planetary conflict is right or wrong, or is that for them to decide internally? What is the measure of humanity and how would it be applied across politically constructed borders? Major Kira was once labelled as a terrorist, as were members of the Maquis such as Chakotay and Cal Hudson. By the way, does anybody know if Chakotay actually had a first name? Or was Chakotay his first name, not his last which I has assumed? We might not know his last name, it could also have been his middle name. 
