The list of armor proficiencies in the druid class description (PHB, p. 65, or here in the basic rules) states:

Armor: Light armor, medium armor, shields (druids will not wear armor or use shields made of metal)

According the Sage Advice article from March 2016:

Druids don’t lack the ability to wear metal armor. They choose not to wear it. [...] If you want to depart from your class’s story, your DM has the final say on how far you can go and still be considered a member of the class. (emphasis mine)

Does this mean that an AL druid can choose to wear metal armor, because it is not stated that wearing metal armor is forbidden?

Adventurers League plays by the rules of official books; it does not acknowledge supplements like Unearthed Arcana or Sage Advice.

So the rule from PHB is:

Druids will not wear armor or use shields made of metal

Therefore, per AL, per PHB, no, a druid wearing metal armor would not be allowed by the AL.

Probably not, because that's a house rule.

From the AL FAQ:

House rules, that is to say rules that you create
that aren’t in the official materials such as critical
fails, new races, new classes, etc., aren’t permitted
for use in D&D Adventurers League play; the
Adventurers League uses the rules as presented in
the PHB.

and:

The only optional or variant rules available for use
are:

• Variant: Customizing Ability Scores (PHB)


• Variant Human Traits (PHB)


• Half-Elf Variants (SCAG)


• Option: Human Languages (SCAG)*


• Tiefling Variants (SCAG)


• Variant: Playing on a Grid (PBR)


• Variant: Skills with Different Abilities (PHB)

That said, that only applies to legitimate, published variant rules. The issue of outright breaking the rules, e.g. putting your druid in plate, and the DM just winking and allowing it, is not addressed.

Since you're going to hairsplit between "will not" and "cannot": strictly speaking, your druid has the ability to wear metal armor, but you're not allowed to have them wear it. Druids not wearing metal is a lifestyle choice, not something forced on them. However, for rules purposes, they are required to make that choice and follow it.

You can choose, so long as you are willing to stop being a Druid.

From "Rules Answers: March 2016" on the WotC D&D website:

What happens if a druid wears metal armor? The druid explodes.

Well, not actually. Druids have a taboo against wearing metal armor
and wielding a metal shield. The taboo has been part of the class’s
story since the class first appeared in Eldritch Wizardry (1976) and
the original Player’s Handbook (1978). The idea is that druids prefer
to be protected by animal skins, wood, and other natural materials
that aren’t the worked metal that is associated with civilization.
Druids don’t lack the ability to wear metal armor. They choose not to
wear it. This choice is part of their identity as a mystical order.
Think of it in these terms: a vegetarian can eat meat, but the
vegetarian chooses not to.

A druid typically wears leather, studded leather, or hide armor, and
if a druid comes across scale mail made of a material other than
metal, the druid might wear it. If you feel strongly about your druid
breaking the taboo and donning metal, talk to your DM. Each class has
story elements mixed with its game features; the two types of design
go hand-in-hand in D&D, and the story parts are stronger in some
classes than in others. Druids and paladins have an especially strong
dose of story in their design. If you want to depart from your class’s
story, your DM has the final say on how far you can go and still be
considered a member of the class. As long as you abide by your
character’s proficiencies, you’re not going to break anything in the
game system, but you might undermine the story and the world being
created in your campaign.

The Adventurers League advice given in other answers follows the party line. So, you can't choose to do it, and remain a druid. If you have some special reason, you can beg your DM.

The other answers are almost all incorrect. The official Sage Advice Compendium from WoTC (this is different than the Sage Advice website, which merely collects tweets by the designers) is RAW according to WoTC, and clarifies RAW. In addition, that document also states Jeremy Crawford's official responses are also RAW.

The Sage Advice Compendium clarifies further that Druids can wear metal armor, it is just taboo. It would be fine for a DM to make roleplay consequences for wearing metal armor, such as disadvantage to social checks with other druids. However, if a DM doesn't like that and rules the Druid cannot wear metal armor, then it is a houserule. An Adventurer's League DM should allow a druid to wear metal armor.