Does hexproof prevent an opponent from targeting a creature with a copy spell like Fork?

Hexproof is defined in CR 702.11a: a permanent with hexproof can't be the target of spells or abilities your opponents control. This is a blanket restriction on targeting — it does not matter what type of spell is doing the targeting.

Fork (and similar copy spells like Twincast or Reverberate) don't copy a creature directly; they copy an instant or sorcery spell that is already on the stack. If that original spell targeted a hexproof creature, the copy also needs to target something. When you cast Fork, you choose new targets for the copy if you wish — but if the only legal target you want is a hexproof creature controlled by an opponent, you cannot choose it because hexproof bars that targeting (CR 702.11a, CR 114.9).

If the original spell targeted the hexproof creature (perhaps cast by that creature's controller, who is not an opponent of their own permanent), the copy created by an opponent's Fork must choose new targets. Since the hexproof creature is off-limits for the opponent controlling Fork, a new legal target must be found or the copy is simply cast without targeting the hexproof creature.

Concrete example: Your opponent casts Lightning Bolt targeting your Carnage Tyrant (which has hexproof). You cast Fork targeting that Bolt. The Fork copy needs a target — you cannot choose Carnage Tyrant as the target for your copy because Carnage Tyrant has hexproof and you are its opponent. You must pick a different legal target or acknowledge the copy cannot legally target it.

Note: hexproof only restricts opponents. A player can target their own hexproof permanent with their own spells and abilities (CR 702.11a).