One of the signs of healthy emotional intelligence is the ability to be "self defining" - having one's own view and opinion of situations and people without being "drawn into" the opinions or issues of others. Both emotional triangles and enmeshment are signs of poor EQ, whether by the one who does the triangulation or the one who is drawn into the triangulation.
For instance, it is not unusual for someone who has an "issue" with another individual to seek to draw other people into their "issue" by speaking ill of them (often subtly to first see if there is resonance) and looking for others to join them in their opinion. This makes the one with the "issue" feel better (they have others who now share their opinion) and it allies others with them against the one with whom they have an issue. It can be very subtle but the results are not!
This often happens in families, in workplaces, in ministries and in congregations. It divides people, hurts relationships and can cause relational chaos on a team or within a group. And it is a sign of poor emotional intelligence on the part of the perpetrator as well as those who choose to join the perpetrator.
Individuals with healthy emotional intelligence keep their own counsel on people and situations. They do not allow themselves to be drawn into alliances with others against others. They are able to think for themselves and understand that they are responsible for their relationships with both parties and they do not allow others to define those relationships for them.
In addition, they immediately recognize when someone tries to "draw them in" that what they are hearing is probably not reality - that there is a reason that they are being lobbied toward a certain view or attitude. In fact, rather than being drawn in, emotionally healthy individuals immediately recognize that they are dealing with someone with poor EQ and they are wary of the information they are receiving.
How can one deal with situations where one is being subtly lobbied to agree with one party against another (triangulation)?
First, understand that your responsibility is for your relationships and that you need to be "self defined" and come to your own conclusions about people and situations. Healthy self defined people do not allow others to define reality for them.
Second, realize that anyone who triangulates is not operating out of healthy emotional intelligence and rather than solve the issue they have with others they instead seek to ally others with them against those with whom they have issues. Think about the difference between those two approaches! Which would be the biblical approach?
Third, do not give sympathy to the one seeking to triangulate which only feeds their unhealthy practice. Instead, ask clarifying questions that might help them understand that their perspective may not be the only way to look at the individual they are unhappy with and encourage them to deal with the relational disconnect rather than to draw others into their issue. When we give sympathy in the absence of personal information we become complicit in the problem.
Fourth, ask who could meet with the one with the offense and the one who is being marginalized by the one with the offense to bring understanding and reconciliation. Their willingness to deal with their issue when called on it will tell you a lot about their real motives.
Don't get caught in the deadly web of triangulation. It is unhealthy, it destroys relationships and it hurts ministry. Furthermore it is a sign of poor emotional intelligence and the inability to be self defining.