Do crabs carry disease?

Not typically: Crabs are an infestation, usually, but not always sexually transmitted. The intense itching will usually drive people to seek evaluation and treatment. Scratching of the itch can cause a secondary bacterial skin infection. Contracting any std markedly increased your risk of having other std's, even if the "crabs" don't carry the other disease, you can catch more than one at a time.

Not typically : Lice infestations can result in secondary bacterial infections due to scratching.

Pubic Lice: Pubic lice may be seen in conjunction with other sexually transmitted diseases. Secondary bacterial infections may occur. Although lice can transmit diseases such as epidemic typhus, trench fever & relapsing fever, I don't believe that this really applies to pubic lice in particular.