The only times in the game when you are supposed to wear something specific it is handed to you by friendlies before you need it. The neural interface suit for Operation Anchorage and the vault 112 suit for the Tranquility Lane quest (not sure if you are actually required to wear this one or not). In all other cases you can use whatever armor/clothing you like.
The vault outfits are never required in order to be effective in combat. The armored 101 suit is useful in the early game because that early it is not easy to find better armor, but the moment you gain access to something better you can feel free to abandon it.