From the desciription you gave in the OP and not being nosy enough to hunt it down it seems to be the case of the storm in the teacup that somehow managed to sink the ship. Unfortunately there seems to be a highly negative connotation to conflict even though it is a natural norm of human interaction, however the type of conflict often defines as to whether it can be constructive or destructive and consequently how you should go about handling it. Whilst I haven't GMed properly in a while due to time constraints, much of it ties into simple theories of people management and leadership. As a simple fact a blanket, one-size-fits-all style doesn't exist as there's always differences in both the GM and their player which can often call for differing styles. For example, two writers clash over a character leads to the situation where it can either go personal as "you stole my character" or impartial as "it seems a little close, would change be possible?". In my opinion, being a great GM isn't a matter of having one absolute style and sticking to it but rather being able to meld and adapt to both different situations and different people.

 As far as the role of a GM, I believe it extends beyond that of simply having a good story or running a tight ship because in my opinion they should also foster a sense of community. This sense of belonging and personal attachment often proves a boon when trying to build both loyalty and trust with your players and from your players to you. I often find this focus on community/personal connection that if often missing in GMs; sure they give a good plotline and manage to keep people on track but do you really feel like you belong to this roleplay or even feel valued?

To cut it back to the basics skills I'd have to cut it down to the relatively simple and very learnable set of communication, adaptability and commitment to your beliefs and values. 

Communication has to beat about personalising interaction and depersonalising criticism; when you review something it's the idea not the person behind the idea. When you chat with someone, you talk to the person and appeal to them in a style that suits them. Whilst this is hard to do without personal rapport or history, there's often slight nuances in the way they right or how they portray themsleves in an OOC that often gives away how you should interact with them. Learning it from naught is simply about trial and error with experiencing teaching you what is appropiate for who. 

Adaptability ties in well with both contingencies and compromise, that is being able adjust yourself to the situation and the people in order to produce as many postive results from wherever you may find yourself. This can range from being flexible on posting cycles to accepting a character that may not slightly fit your vision/acceptance crtieria (within reason and with a lot of personal explanation). The only danger with adaptbility is potentially being viewed as treating people differently to the others and as such may find a non-existent bias in your style or even worse, potentially discover a bias (which should be avoided).

FInally, commitment to your personal beliefs isn't making it all about you but rather recognising the fact that as a writer you have certain standards which must be uphold, both IC and OOC, along with a style of play that appeals to you. Whilst the personal appeal may seem rather self-centric it is crucial as it motivates you to stick with the topic because it becomes a creature of your own mind, even despite the input of others and as such a sense of ownership will most likely be instilled. What'll you'll often find is that with every successive rolelay, whether a success or failure will build your repertoire and understanding.

That brings me to my overaching thought, there isn't a one-shot-to-wonder method of GMing, it's an interative process where you only hope to get better as you go along along with producing some truly memorable quality!