Dumbledore will gently remind everyone that everyone in this room was hand chosen for their talents, for their goodness of spirit, and for their strength of belief, and though there are many differences between us, we must look to the strengths of our allies and not judge differences as weakness.
"For we are not like the death eaters, who seek to hate and destroy all that is different and create a society of sameness. We must be better than that," and here he would smile at the Ravenclaws and the Gryffindors, who are obviously fighting, "even if it is quite aggravating."
He'd also say that he doesn't expect the Order to be the best of chums, but to have enough respect for fellow members to consult with them and freely share information. A hand with fingers going in all different directions can do very little for good.