Being a member of NATO is something that helps unify countries and create a sense of protection within them. As such, this membership helps countries progress into modern society, which tends to be fairly liberal. When national security no longer becomes something at risk, it is easier for the country's population to move forward socially.
Countries that join NATO become more liberalized because they embrace a fundamental concept of liberty. NATO members engage in trade with one another and such economic freedoms increase the living standards and the autonomy of each member nation's citizens. This enhanced economic freedom liberalizes the nations which embrace those ideas.