The following issues are present in all game modes (Singleplayer, multiplayer hosted, dedicated server). I am using a controller, so these may also be specific to that.
Attaching a weapon to your back renders that weapon unusable. Trying to equip that weapon from either the dial menu or directly from the inventory will equip the weapon visually. When you try to attack, your character defaults back to bare hands. Have tested with two handed and single handed weapons. Moving an item to the floor or a container, and then equipping it normally fixes this issue.
Similar to the above issue, attaching a hammer, wrench, or similar item to a belt renders that item unusable for both attacking and crafting. Trying to use carpentry will result in the item not being built (instead, hanging when the animation for using said item should play). Trying to use an item for vehicle mechanics (Removing a battery or door for instance) results in the action being stopped when the animation for using said item should play, and no part is installed/uninstalled. You also cannot remove the tool from your belt directly. You must unequip the belt, and the items will work normally.
*Please disregard the above, it appears it is mod related. Disabling all mods fix these problems.
*Edit 2 - Specifically, it is the Rifle Slings mod.
Also, it's been reported already, but moving items between equipped containers (Backpacks, fanny packs, main inventory, floor) does not work. The entries are in red, as if the game is checking the object for available space and failing the check. Bags or containers have plenty of available space.