Add feta, cream cheese, garlic and oil to a food processor; process until mostly smooth, about 2 minutes, stopping to scrape down sides as needed. With the processor running, slowly drizzle cold water through the chute until a smooth whipped dip forms, 3 to 5 minutes.
Transfer to a serving bowl; top with pomegranate seeds and pistachios; drizzle with honey. Sprinkle with thyme leaves. Serve with warm pita wedges.
