You don’t really need Squeezelite to stream Airplay. Shairport should be sufficient for that. The best thing to do is to try removing Squeezelite from the autostart and stop it so that the two don’t get in each other’s way.
Apart from that, you could also try using plugins for the Squeezebox server to get Airplay to work. Here you can find more information about the possibilities: https://www.max2play.com/en/how-tos/howto-airplay-with-max2play/