Joining an alliance is pretty much the way to not be neutral. They signed a treaty in 1955 to end allied occupation, with the condition that they don't join an

Joining an alliance is pretty much the way to not be neutral. They signed a treaty in 1955 to end allied occupation, with the condition that they don't join any alliances. The intent was that this would prevent them from joining with the Soviets. Times have changed, but the treaty has not, so they are not allowed into NATO since it is an alliance. I'm sure if they really wanted to join all the former Alliance signatories (which are now part of NATO) would be willing to renegotiate the treaty and let them in.