He'll just drop it, and it'll say he can't wear it.
Just lost NCR Ranger patrol and the Veteran Ranger armor.

You shouldn't have lost them. They just drop on the ground right there. You could have just picked them up. They will still be where they were since the game is persistent.

It is a bit annoying though. I don't give a crap if they can't wear it, they should still be able to carry it in their inventory. I mean, FFS, ED-E can't wear ANY armor or use ANY gun; so why would I need to be reminded of this and just have him spit the stuff back out at me?

If you're playing on the PC, there is a mod that allows him to carry faction armor.

http://newvegasnexus.com/downloads/file.php?id=34912

I wasn't thinking at the time, and didn't know they had dropped. I have zero clue where he dropped it

That's pretty stupid, since ED-E can't wear any armor - lazy programming

I would assume that Rex has same problem??

More like careless scripting, shouldn't have autoequip as a Robot/Creature

I have Boone and he can wear some power armor but some he just drops and he can wear ncr ranger stuff.