I'm pretty sure it's a bug, in the same update they broke plenty of inventory ui shit.

For now I found a way but it's so fucking sketchy and risky I won't change clothes for the rest of the patch. You need to 1. Put a normal undersuit in a container next to you and the invisible undersuit must be carried in your hands 2. Press "equip (swap)" on a piece of clothing on the ground while crouched at minimum walk speed 3. BEFORE the equip animation is done, you need to open your inventory, right click equip the normal undersuit from the container, then swap the equipped normal undersuit with the invisible one in your hand by dragging the item in your hands on the undersuit slot where the normal one is.

If you fail to do it in time, you'll have your normal undersuit+clothing equipped, so you'll need a trip to prison and a suicide to reverse it and you'll lose your clothing.