Thorney Island closed, in 1976 and not in the 90's as mentioned somewhere above, as part of the 1975 Defence cuts and was a cost saving exercise as it was no longer required following the phase out of the Andover C1 fleet as tactical transports, and the reduction of the Hercules fleet. It was one of 12 stations in the UK announced as closing at the time.
I doubt if proximity to Gatwick had anything to do with the decision, the only issues that the station had in it's recent years were the many and vociferous noise complaints from the locals.