how do I use X1 with different wifi network?

X1 requires Comcast Internet for the apps to work, even though XG series boxes do have their own modem. It's due to the fact that they are treated as any streaming device, and using them on an X1 box counts toward any data cap.

If you want to use streaming apps, you will need to use something else. A Smart TV, Roku, Fire TV, Google TV, Apple TV, etc...

Concern moved here to the X1 help section for assistance.

Hello user_76gtkg

I apologize if there is any confusion with our X1 service. Though with Comcast Internet your X1 will be far more robust, our internet is what provides this app access. Your grandparents can have standalone X1 service at their home. Again you may find many limitations in the interface as its full functionality requires Comcast Internet service. I hope this better answered your question. 

This doesn't really answer the question.  Do apps like Disney or Netflix work on an X1 box with Xfinity cable service if the TV is connected to a different Internet service and the customer doesn't have Xfinity Internet?

No. You must have Comcast Internet to use apps on an X1 box.