Yes and no.
Yes if you apply scientific theory to magic which is iffy at best.
Here's an alternative approach leading up to a "No" answer:
The item is not meant to be "gamed" using real life physics. There is no rule in the game that discusses the property of clothing. The cube's rules never discuss physical effects such as heat exchange or lack of air. Setting the cube to "block non-living" doesn't mean you eventually burn up since heat can't diffuse out, or that you suffocate since new air can't get in. If those results were intended, the item would say so.
Blocking the non-living clearly are meant to be in opposition to blocking living material (the next effect). This means that blocking non-living blocks arrows, zombies and thrown boulders. Blocking living blocks town guards, goblins and umber hulks.
So the answer is "no". If only naked living beings could pass through, the text would say so.
The fact a living human wears clothing changes nothing and is entirely inconsequential. Why? Because any other answer would make the game fall into a rabbit trap of evermore complicated interactions that only end up making the game impossible to play.
At some level we all need to accept that magic doesn't work like physics.