Yes, enchantments already cast and resolved still continue to take effect.
There isn't much about Curses in the Rulebook, because they operate identical to Aura's, but it doesn't take away that it is its own subtype.
Rulings clarify that:
17-10-2013 A Curse spell targets the player it will enchant like any
other Aura spell, and a Curse stays on the battlefield like any other
Aura. If the enchanted player gains protection from the Curse’s color
(or any other characteristic the Curse has), the Curse will be put
into its owner’s graveyard.
In the Comprehensive Rules it states:
303.4. Some enchantments have the subtype “Aura.” An Aura enters the battlefield attached to an object or player. What an Aura can be
attached to is defined by its enchant keyword ability (see rule
702.5, “Enchant”). Other effects can limit what a permanent can be enchanted by.
So Curses like Aura's target an object or player depending on what it says on the card.
Aegis of the Gods grants the player Hexproof.
702.11c “Hexproof” on a player means “You can’t be the target of spells or abilities your opponents control.”
So while Aegis of the Gods is on the battlefield you can't target that creatures controller.
But what about all the curses you already cast and resolved before Aegis of the Gods entered the battlefied?
Hexproof doesn't dispel or disenchant any enchantments. It just prevents an object or player from being targeted while hexproof is in play.