I know that halflings can hide behind people, that's their special thing. But could a Small-sized non-halfling with Skulker hide behind a Normal-sized party member and claim the partial concealment needed for a Stealth check? This feels cheesey.
Being behind another creature does not allow you to hide.
To attempt to hide from a creature you must be not be seen by it (PHB p. 177). The Skulker feat allows you to try to hide when you are lightly obscured from the creature from which you are hiding (PHB p. 170).
A lightly obscured area is defined as such:
Vision and light (PHB p. 183)
In a lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage on Wisdom (Perception) checks that rely on sight.
Dim light, also called shadows, creates a lightly obscured area. An area of dim light is usually a boundary between a source of bright light, such as a torch, and surrounding darkness. The soft light of twilight and dawn also counts as dim light. A particularly brilliant full moon might bathe the land in dim light.
A character sitting behind another one (be it an enemy or a friend) - regardless of their relative size - benefits from half-cover (PHB p. 196). This does not affect the lighting conditions and visibility of the general area (unless the creature you are hiding behind is accompanied by a dreadful aura of darkness, but in that case you or your enemy probably have bigger problems on your hands).
Hiding behind other creatures was clearly meant to be "the thing" for halflings, so allowing it for any character would be taking away from their flavor.
It's up to your DM
The rules for Hiding state:
The DM decides when circumstances are appropriate for hiding.
The only constraint is:
You can't hide from a creature that can see you clearly
One person usually can't hide behind someone else. However perhaps a skinny person could hide behind a fat person. Perhaps a person could hide in a crowd of people. Perhaps someone could drop prone and hide behind someone who is sitting. It depends on the situation, which is why it is up to the DM.
Now, let's cover a few misconceptions:
- Cover has little to do with being clearly seen. If I stick just my head out of cover, you can see me clearly.
- Lightly obscured refers to things like dim light, light fog, etc. Your entire self is obscured to some degree.
- The Lightfoot Halfling's Naturally Stealthy rules do not retroactively change the basic rules.