"This campaign is about heroes fighting cultists and stopping their plans."
That statement is actually sandbox/linear neutral. Rather, it is firm scene framing that defines what is in and out of bounds & where the group's focus will be on most gaming sessions. IME effective scene framing is more important than whether an adventure is presented as sandbox or linear, because it gives a clear impetus for the players, and evokes ideas about how their party is connected. Even veteran gamers sometimes need a push here so the session doesn't devolve into screwing around doing nothing.
I also think you may be setting up "linear vs. sandbox" as a binary 0-1 situation, whereas I would describe it as a spectrum. Just as you can have lesser and greater infinites, you can have lesser and greater sandboxes. If the adventure is framed to be "against the cultists", for example, then the adventure isn't doing anything wrong by assuming in any given situation the PCs will tend to oppose the cultists. Just because there are boundaries doesn't mean that there aren't sandbox elements: multiple end game scenarios, adventures that can tackled in various orders, challenges with multiple possible solutions, recurring adventure sites & NPCs that change over time, big decisions for the PCs to make that effect the rest of the adventures, etc.
I don't have Hoard of the Dragon Queen, so I'm speaking abstractly here.