Many people go to extremes to avoid any sign of disagreement or the appearance of conflict. It is tough for people to learn how to disagree without fighting. In conducting meetings, you hope that conflict will not occur, but if it does, don't be afraid to deal with it. A meeting which airs differences of opinions and exchanges of strongly held beliefs is a good meeting! You got to the heart of matters, and people spoke truthfully. Strong disagreement can generate emotions, but it can also engender deeper thoughts on the issues.
It is important, though, that the opinions and exchanges be controlled, and that's where you come in. Insist that participants stick to the agenda items and the content provided there and prevent personal remarks of any sort . If people bring hidden agendas or unresolved emotional issues to your meeting, contain the contribution of their "baggage" but encourage their thinking and responses to your meeting content.