How to hide selected rats nest lines in Altium?
There is a shorter/quicker way than @Rev1.0's as well:


Right click the net you want to hide
Go to Net Actions in the menu, and press Hide Nets.


Shortcut (as everything in Altium has a shortcut): 
Right-click, N, H.

Image showing this by Bence Kaulics on a different question here on the site: