Is it rude that my boyfriend texts/IMs other girls while he's with me?

This should be a no brainer question, but it's a little more than that. I'm not threatened by many of these girls as he's told me who they are, and I've met a few (though I'm sure there's more than just those ones, because I know he knows a LOT) and sometimes when we're out and I'm driving him around someone will IM him and he'll conversate, or texts when other people text. I mentioned it once and he toned down a bit, but he still does it occasionally. What to think?