As of today, the SwipeableStack swipes child in any direction. If you ever need a swipeabled child that can only go left or right you can't use the SwipeableStack and need a custom widget instead.
This is unfortunate because the SwipeableStack is a nice addition, however most use-cases don't need to swipe in all four direction, making this widget almost useless for now.
You can use a custom widget, Flutter have many options to build or import a swipeable stack. However, as the widget is already integrated in FlutterFlow it would be best to finish its implementation and add the option to prevent given swipe directions.
I can see in code you are using the flutter_card_swiper which already implement the options to only enable given direction with allowedSwipeDirection. This is your chance for an easy win that would benefit your community.
This is not the first time this issue is encountered: https://community.flutterflow.io/ask-the-community/post/lock-swipe-direction-of-swipeablestack-lyeTxe7zDm9DRk0
