In principle, if a disagreement is caused by an outside issue that has nothing to do with the group issue at hand, then it must be dealt with outside the group.
An outside issue is a disagreement because of, for example, some incident between the parties that happened years ago and was never dealt with, or because of a mental disorder or perhaps an addiction. Or perhaps the conflict is related to a misconception closely held since childhood or an illogical fear.
Outside issues are usually personal and often completely unrelated to the group’s immediate business, although they can get hugely in the way of the group’s immediate business. Outside issues prevent people from seeing or acting clearly.
If an outside issue is in the way, agreement will only come about if the issue is dealt with. If an outside issue is not dealt with and disagreeing parties are unable to let go of the issue, then the group is at risk of being paralyzed, held hostage by an issue that they have no ability to fix.
Practical Tip: Once you recognize that an outside issue is the cause of a disagreement, encourage the parties to deal with it outside the group. Perhaps mediation is called for, or perhaps therapy.
If those with outside issues are unwilling or unable to get outside help, take a vote, bring in an arbitrator, or have somehow otherwise resolve the issue — even over objections. Someone might lose but losing is not always bad. Sometimes it’s the only thing that will allow some people to move forward.
It is better that one or two people lose a single issue than for the group as a whole to get bogged down and unable to make progress.