Questioning
Another approach is to switch your team's focus from conflict to "research." Encourage people to provide information, rather than state that they're angry or disagree with something.
To achieve this, use some carefully phrased questions. Don't just ask yes-or-no questions – try to clarify what people are thinking. Ask for specific examples, and perhaps suggestions for how the "disagreeable" idea would need to be changed to make it acceptable to them. In some cases, the alterations they want may be quite small.
When a conflict arises in a meeting, you, as the chair need to take control. Don't let others start wading in to the conflict by interrupting you or the speakers.