Does the distance between the signal lines (in terms of noise immunity) matter when wiring the board?
Cross-talk can be a problem when two tracks that carry unrelated signals are too close. However, when two tracks are carrying a differential signal, placing the tracks closer together usually improves immunity from unrelated signals.

Placing differential tracks at the right distance relative to each other (neither too close nor too far) allows the "transmission" to have a "purer" characteristic impedance and thus signal reflection problems are reduced.

So, given what I've said, you have to categorize what the signals are before deciding on how to track them. I notice that in your screenshot of the PCB, one track is called TXD and another is called RXD. This implies to me that it is likely that the signals they carry are electrically unrelated and therefore they should be kept apart. However, if you run a ground track between them, they can be closer (for example).