Just like it was the case with previous, similar polls organised by the government , the 2015 Hungarian national consultation on "immigration and terrorism" arose significant data protection related worries in the public opinion. Indeed, governments organising such consultations are given an opportunity to collect political data on their citizens, and store them into a database. Yet, such experiments in digital direct democracy are increasingly frequent. For example, last year, the French government launched a large-scale Internet consultation on a proposed Bill on digital rights. This paper studies the compliance of Hungarian and French governmental consultation practices with data protection requirements, both legal and technical. Are the personal data of citizens handled in conformance with national and European regulations? This paper describes the tools and methods currently implemented to protect citizens' political data in public consultations, and explores ideas derived from computer science and legal literature in order to improve the level of data protection in digital democracy.