You can say that iron triangles are a threat to democracy because they allow small groups of people to take control of government in a certain area. This prevents the population as a whole from exerting its power over that policy area.
For example, if there is an iron triangle with regard to agriculture, only farmers and their interest groups will have a say in farm policy. They will work together with the government agencies and the Congressional committees in this policy area to enact policies that they like. They can, for example, keep giving themselves subsidies that most Americans would not approve of. Because there is an iron triangle at work, only the voice of the small group is heard and subsidies are given even though the majority opposes them. This is, one can argue, a threat to democracy.