There is two super easy way to fix it:
1- Give them only proficiency in Light Armour and Hide Armour. That means that, if a Player wants to play a tin plated Druid, they totally can, they just need to find the proficiencies elsewhere and there's no question that needs to be asked about materials or multi classing or whatever. It just works like every other damn armor proficiencies, even if a little weird.
2- Make it so they can't use Wildshape while wearing metal armor (while having a sidebar in the armor section about alternate materials) or even while wearing anything with a higher AC than Hide. That way, non-Moon Druid could have a decent choice.
You could also make it a purely narrative detail and not care that every Druid end up in half-plates but that's not a popular answer.
You could also give the Druid a kind of 'unarmored defence' that stop working if they get someone better than Hide armor.
It's really not that difficult.