Would that not be illegal? Or is SpaceX required by law to do so?

The law prohibits employers from hiring only U.S. citizens or lawful permanent residents unless required to do so by law.

http://www.eeoc.gov/laws/practices/inquiries_citizenship.cfm

On the front end it's pretty cool since you are targeting internal tools you can assume modern browsers and use the latest frameworks and tech with zero legacy support to worry about. We look for people who have full stack experience and can be flexible and help out on any area of a large web application (including a some ops and continuous integration). Communication skills are super important - usually these projects are on small teams that need to work well together and support people within the company who use the tools. We also try to make sure people are good with details and are thorough in their ability to properly build and test their stuff - these tools are critical for the success of the mission so they are every bit as important as the code on board the vehicles.