You have to understand Druidism in terms of general animism. In point of fact we don't actually know anything about Druidism because it left zero trust worthy historical records and pretty much everything that everyone thinks they know about it is the product of some much much later invention. We do know abit about general animism because in some places it survived to modern times, and we know something of the sort of animism that must have existed in Europe before it became polytheistic (and latter monotheistic). We don't however even actually know to what extent ancient druidism was animistic, and its entirely possible it was a more modern sort of polytheism with an emphasis on 'big gods' rather than 'small' ones. We just don't know.
But in terms of the 'don't use metal' prohibition, it makes sense if you look at the world in animistic terms. The the animist everything in the world is magical. Things don't fall because of gravity, but because it is the nature of earth spirits to pull things to the ground. The wind doesn't blow because of temperature differentials but because wind spirits push it. We in the modern world look at everything as being governed by shared laws that effect everything. The animist does see any shared laws, and instead sees everything as acting according to internal spirits. Rocks are rock like because a rock spirit makes them that way. Apples are sweet because they have 'appleness', not because they have sugar. And so forth.
Under this view of the world, it is possible to see metal as inherently evil. Animists tend to percieve metal as 'dead rock', or maybe more accurately as 'undead rock', where the spirit in the rock is killed by the fire and beating that is applied to it. It gains its power and strength by being dead and sharing its 'deadness' with other things. That's why metal is so useful for killing things. Thus, iron, which is the most clearly 'unnatural' metal is percieved as being deadly to spirits (like faeries) by virtue of its lack of internal magic and the deadness it carries.
D&D in 3e screwed this up completely. 'Cold forged iron' is ordinary hammer tempered steel. Most metal swords not made of special materials would qualify. But the 3e designers didn't understand the term of artl, and so invented this special class of metal called 'cold forged' that was created by a highly magical process in a highly magical place. This utterly inverts the mythology, making the metal dangerous to spirits by virtue of its magical nature rather than by virtue of its unmagical nature.
In modern terms, the closest you can get to this is certain strands of the environmental movement, which personify 'Earth' and see the natural world as being inherently good and technology that disrupts the natural state of the world as being inherently bad.
Of course, the thing to keep in mind is that since we actually know nothing (and I do mean nothing) about real druids, it's highly likely that once again what we think of Druids is being colored by modern perceptions. The northern Reinnasance created most of what we know about Druids whole cloth to be exemplary of the sort of enlightened natural philosophers they wanted to be and to be a nationalistic and ethnic counterpart to the ancient Greeks and Romans claimed in southern Europe. The druid got dug up again and reimagined in the 19th century. The modern neo-pagan and environmental movements do much the same sort of invention to suit their own causes and things that they want to believe about their heritage. It's a blank slate.
