Why did the Elven army turn to face Legolas and Haldir when they greeted each other?

This is never elaborated on in the movies, nor can I find any explicit interview that answers this question.

However, Legolas is royalty (as the prince of the Woodland Realm), so it would make sense for the Elven troops to acknowledge him; at least more so than Aragorn, who at this point is not yet widely known nor treated as having any royal importance).

Secondly, it may be a matter of marching protocol that the troops only turn once all of them have come to a halt (for the same reason why armies march in sync and stick to formations - to convey the image of a well oiled machine).

When Haldir starts speaking, the troops are still marching. The troops behind Haldir did halt earlier than when they turn to face left; but it's possible the troops in the back were still filing in (we don't see them on screen), and the elves only turned when all troops were halted.

Paulie_D may also be right that the elves' response may be related to Haldir speaking to Theoden (i.e. the order of business), rather than Haldir having just greeted Legolas (i.e. a personal interaction).

When Aragorn greets Haldir the army doesn't move but when Legolas greets Haldir the army turns in unison to face them.

I don't think this has anything to do with Legolas as they don't do this until after Haldir & Legolas have greeted each other.

I suspect that this is more to do with the Elves turning to face Theoden to acknowledge their commitment to the fight.

Haldir indicates this by saying..

                                HALDIR
                     [Turning to Théoden] We are proud to 
                     fight alongside men, once more.

It's a display of force and a sign of respect. Remember, when Theoden comes into frame, the Elves turn in "Salute" to the welcoming monarch.

They turned to Legolas. Theoden and Aragorn are both shown in the scene before elves turn to salute. Theory that they are waiting for everyone to fill in is not valid. If they are walking in a column, as they are, they don't to wait for others that long. If it was the case, I'm pretty sure Haldir would take a waiting stance until he can 'properly' do it. If they wanted to show respect to Theodon, why did they wait until Legolas? You can clearly see they start turning around the same second Haldir and Legolas exchange a manly only arm hug. Then in the next frame you see Legolas standing behind Haldir and smirking happily like a kid. Since Haldir isn't there in the books, I they simply wanted to put more elves in the story. That scene and the whole battle work for me since I first watched it.