if I leave the faction that is currently is manager of my producing shipyard, will the production abort because I leave ? or it'll still continue until completion ?

It will continue until it reaches completion. Then if the operator is still you and you are not in the faction it will pause, requiring someone that is a member of that faction to pop over and restart it to finish it off.

if you leave the ship faction, make someone who is in the faction operator, so when it does come to completion all will finish as normal.