There is a radius around a player that protects objects owned by them from being picked up. If you are playing with friends, you should add them as friends so that they can pick up your items and you can pick up theirs when you are in close proximity to each other.

Default settings should suffice for most situations, but if you need additional permission options you can set friends to one of four permission groups. Go to your character window (C) and right click on lower left or right to get a menu. Manage, Friends to set the group to Trusted, Friend, Contact or Other.

It is necessary to add Modify Building permission for players to be able to build inside a building.

On a settlement you need to enable the Pick Up permission for a player to be able to use a hitching post. For non-citizens create a new roll. Settlement, Manage Roles, Add Role (upper right), enter a Role Name (I typically use the player's name) in the first field and the player's name in the Player (third) field. Check the permission box for Pick Up and Save.