We always considered stall doors/gates/screens to be best hanging where they open both ways or to the outside, NEVER the inside, as a basic, common sense way to hang them in the small spaces stalls are.
The reason, if you have a horse struggling, sick and falling into things, scared and trying to get out, colicky and keeps going down and flailing, you don’t want to have to push anything into the stall to try to get to him, or if you were in there with him, find a way to get that open and to get around it to get yourself out.
We have one door to the outside that we could not open out in our barn because of a column.
We do open that one to the inside by necessity, but it never is used to go thru it, is one that either stays open into the run, or closes the stall, is not a walk thru with a horse door.
The front door into the aisle is the one to lead horses in and out and that one opens into the aisle, not inside the 14’ x 14’ stall.
When we used screens on an open stall door, those were hung where they didn’t fold back, so they opened both ways, in and out.
We always opened them out to get a horse in and out of a stall, never into the stall, where they could have been in the way.
How to hang swinging anything in horse stalls is very much, every place and continent I have been in, standard to open to the outside of stalls, because it is what makes most sense, when you have a small space and the large mass of a horse to move around in there.
You don’t want anything possibly in the way in that small space.