I tested the whole thing again with your setup (and an iPhone 7). It worked for me that Airplay interrupts the playback of Squeezelite. And this is exactly what should happen when you enter the server IP in the advanced settings of Shairport. If you stream music via Squeezelite and then connect the player via Airplay and start playback, the Squeezelite stream is interrupted by Airplay. If you then stop Airplay again, Squeezelite playback should resume. However, it is not possible to interrupt Airplay playback with Squeezelite.
When exactly do the dropouts occur? When you change the playback source? Or generally when you stream via Airplay? Are there any error messages in the server log file? You can find the log under Settings/Information.