Yes the book is clear that casting spells requires components, no has disputed that.
True in a sense, the thing in question has always been an interpretation of what they say. What does the action in question look/sound like? By extension is it impacted by things that affect them.
The Druid text is the first interesting piece in all of this. The not casting spells piece doesn't apply because we weren't talking about that in the first place. The easy resolution is they can preform the necessary pieces of the action in beast form, just like the Beast Spells ability grants them that exact ability for the initial casting.
This is all assumption.
Let me add another variation on this. What does taking the Help action look like? Does a character stand around doing and saying nothing and an adjacent character suddenly gains advantage? The book doesn't say you do something anymore than Hex does ("lending aid" versus "cursing"). But, that leads to a pretty silly game world if you follow that thought.