I have found this Q/A explaining some items a Thief can use through their Fast Hands feature as well as this tweet (though now unofficial) from Jeremy Crawford saying that Fast Hands does work with a shield.
The Fast Hands feature's description states:
You can use the bonus action granted by your Cunning Action to… take the Use an Object action.
And then the "Use an Object" section states:
When an object requires your action for its use, you take the Use an Object action…
The DMG (page 141) states this about activating magic items in particular:
If an item requires an action to activate, that action isn't a function of the Use an Object action, so a feature such as the rogue's Fast Hands can't be used to activate the item.
Shields require an action to don or doff and "Shield, +1, +2, or +3" are listed under the "Magic Items" section of the DMG on page 200.
However, it is still unclear to me whether donning/doffing a shield counts as either "Using an Object" or "Activating a magic item", so I am wondering:
How does Fast Hands interact with mundane and magical shields?
Best Answer
You can use Fast Hands to equip a shield.
In the Player's Handbook, on page 193, the Use an Object action says:
A shield is an object, and donning or doffing a shield requires an action, so it seems to fall under Use an Object, just like any other object use that requires an action (such as pouring out a bag of ball bearings). As such, it should be valid for Fast Hands to accomplish that as a bonus action.
Whether the shield is magic or not makes no difference.
Equipping a magic item is not the same as activating it. The Dungeon Master's Guide (p.140-141) discusses "Wearing and Wielding Items" and "Activating Items" as separate headings:
This makes specific mention of donning armor and shields, but no mention of it being anything more than the normal donning action.
Activation is an entirely different sort of action:
and, under the item category listing for Potions:
So "activating an item using an action" is when the item's description or the item's category specifically calls out that activating it is an action.
Arguably, a magic weapon is activated when it is used to make an attack, and magic shields or armor are activated when the wearer is attacked, but whichever way you go on that, it still wouldn't stop Fast Hands from working with the item.