Other mistake: When one of the agents is ambushed by the Tooth Fairies he is reduced to a skeleton, with his teeth still visible. However, it was earlier stated that Tooth Fairies start by eating the teeth, then finish off the rest of a body.
Other mistake: Dating back to the first Hellboy movie, we know that Abe Sapien has very prominent webbing between his fingers (extending almost to his fingertips). However, in the Troll Market scenes from Golden Army, Abe is wearing snug, full-fingered human gloves, which should be impossible with his webbed fingers.
Chosen answer: Why not wear it? It's clearly something that's useful to him, even if it's apparently not particularly essential. It may simply just make him more comfortable, like a human wearing a scarf in cold weather - allowing him to breathe the water that he prefers rather than air. There's never any mention that Abe can only survive for a limited time out of the water; equally, there's no suggestion that he's particularly vulnerable to atmospheric microbes. It's part of his equipment that he uses when he wishes to, that's all.
Tailkinker ★