This is a very interesting question.
I think there is always a potential conflict of interest betwen patron and city, if the two do not co-incide.
I also think you are entitled to know how any city mate will handle that conflict, which loyalty is the stronger, what their patron's views are on killing another order mate, for instance. You can then make a decision as to what extent you can trust them to behave in ways that you find acceptable.
Allys will no doubt respond for herself, but I know she has worked out what she will and will not do for a city enemy who is also an order-mate, and her decisions satisfied me.
I will set out here what my own priorities are so that it is openly on record. My loyalty is to patron, city, guild, in that order.
However, I understand that my Lord Proteus would not object to me killing an order-mate if they were to attack my city. He also does not require me to break my Guild's ban on servicing thieves, despite having a leading thief in a high position in our order.
So, although my patron comes first, in practical terms it makes no difference at present to anything that I do as a Springdalian or a Craftmaster.
I have not discussed killing Parrians with him, as my fighting is still at the stage of trying not to get killed myself rather than aggression towards anyone else!
What will happen in times of war I do not yet know.