That's right; the SoftwareSerial library is not supported by Galileo. However, there is a workaround that might be helpful for you. I uploaded an example code here: Galileo/Arduino-Examples/SoftwareSerial at master · MakersTeam/Galileo · GitHub.
On the other hand, you mentioned that you are having issues using the pins 0 and 1, right? Well, the SoftwareSerial library is not necessary to use those pins. You only have to use the "Serial1" object in your Arduino sketch to send and receive serial data through those pins. Anyhow, I suggest you to take a look at the example above; you will know how to implement a serial interface on pins 2 and 3, and how to use the Serial1 object too.