Originally Posted by Efrem

If they've called your group and you're standing there, what else are they supposed to do? If they're ready to board before you have your act together and start walking, they should board. If that happens to take them in front of you, so be it. As far as they know, maybe you're waiting for someone else so the two of you can board together. (Maybe you have the other person's boarding pass or something. It's not their job to figure out why you're standing there after your group has been called.)

If they've called your group and you're moving, just not moving quite as fast as they'd like you to, it's incredibly rude. You'll probably all end up waiting a bit at the end of the jetway anyhow;

If they haven't called your group, the gate agent should send them back. Granted, not all gate agents do, especially if they're in the next group and it's about to be called, but in that case they shouldn't be going anywhere - and you could perhaps say something.