For RP purposes is it possible to play the whole game though wearing nothing but a factions clothing?? I still want to get the most out of missions and NPC interactions but do it wearing nothing but faction clothing??

Unfortunately no. It took me till I was half way through my Legion run to figure out why they did not like me more. It was because I was wearing Legion armor, and it made there reputation neutral...

It would depend on which faction's clothing you're going to wear and when you're going to wear it.

For example: you are given a Great Khan outfit during Aba Daba Honeymoon when you accept the mission to deliver drugs to Motor-Runner, and wearing it will make the Fiends inside Vault 3 friendly. However, if anyone in the NCR sees you wearing it they will immediately start shooting. As the best access to V3 is via the El Rey Motel and there is an NCR sentinel watching the bridge there, you can easily start a firefight you don't actually want.

More generally: as long as you do not wear gear belonging to a faction opposed to the one you wish to deal with, you'll be fine.

EDIT: What DD says is true, wearing Faction outfits will set your reps to Neutral. You can still finish the game that way, though, since all that matters for faction access is that you not be hated by them, and those few quests that do require decent-good faction rep are either not part of the main quest lines or follow a quest that is part of them that grants a massive rep boost.