When I move the crossfader while using djay, the headphone CUE is automatically switched. Can I disable this function?

Yes. You can enable/disable it as follows.

[djay for iOS]
1. Taps djay icon > Gear icon on the top of the screen.
2. Tap [Advanced].
3. Tap [Auto Select] in [PRE-CUEING].

[djay Pro for Mac]
1. Click Headphone icon on the top left of the screen.
2. Uncheck [Auto Select].

[djay Pro for Windows]
1. Click Menue button on the top left of the screen.
2. Uncheck [Auto-select active deck].