The Crossbow Expert feat (PHB, p. 165) states that you ignore the loading feature of crossbows, but does that mean you still need a free hand in order to reload it?
According to Sage Advice, yes
The article is here:
And the relevant quote is here:
What does that all mean for a hand crossbow? It means Crossbow Expert makes it possible to fire a hand crossbow more than once with a feature like Extra Attack, provided that you have enough ammunition and you have a hand free to load it for each shot.
Yes, because 'Loading' is a very specific term in the PHB
To add additional context. The Feat Crossbow Expert states:
You ignore the loading quality of crossbows with which you are proficient. (PHB 165)
This can be misleading at first, but if you look at the precise definition of loading in the PHB, you will see that the Loading is a specific weapon trait that is a restriction to do with time, not hands:
Loading. Because of the time required to load this weapon, you can fire only one piece of ammunition from it when you use an action, bonus action, or reaction to fire it, regardless of the number of attacks you can normally make. (PHB 147)
As Percival has stated in his answer, the benefit of the feat Crossbow Expert is waiving this limitation. Specifically, waiving the limitation of this aforementioned weapon quality, not waiving the more colloquial definition of 'loading' as the act of putting ammunition into a weapon.
On the other hand Ammunition is another quality which the hand-crossbow has. It is written:
Ammunition. You can use a weapon that has the ammunition property only if you have ammunition to fire from the weapon. ... (you need a free hand to load a one-handed weapon). ... (PHB 146)
RAW the feat Crossbow Expert does not say anything about ignoring the ammunition quality of crossbows.