can you contract crabs or any other STD from getting a bikini wax?

I don't think it's possible. You get crabs from intimate contact with another person - not from surfaces. You cannot get crabs from tables or toilet seats.

I think it would be next to impossible to get any other std from waxing.

The wax is hot, therefore it would kill any bacteria or virus that might be in the wax. (Crabs also die at high temps.) The waxer probably wears gloves, so there would no risk there. I would hope the table or chair you're sitting in is wiped down. If not, it's unlikely that any std would "hang around" on the surface. Most of them die on contact with the air.

I'd say it depends on where you're having your bikini wax done.

If someone turns up for a wax (done anywhere on the body) and there are sores, rashes, bites, etc - a reputable beauty therapist should be refusing to do the treatment and advising them to seek professional medical advice/clearance before rescheduling the waxing.

If you're going to someone who has been professionally trained, it would (in theory) be likely that they would spot anything unusual and the appointment would be over before it began and they would take the appropriate measures to ensure the area was hygienic for the next client.

Pay attention to the 'professionalism' of the staff and look at the state of the facilities. If the staff or the facilities look unhygienic, then I wouldn't stick around.

Crabs are small parasites that attach themselves to pubic hair and feed off of blood. As it is possible for you to get them from an unclean table as well as from toilet seats, it is highly unlikely as you are having hair removed and heated wax is involved. They can be seen upon inspection. I would go to a reputable salon and make sure they use sterile techniques, clean and replace table covers with each client, etc.