At each and every registration of voters held under any of the election and registration laws of this State, whether it is a personal registration or otherwise, and in all cities, counties, boroughs, townships, and all other districts, there shall be a registration and enrollment of the voters according to their respective party preferences and affiliations: Provided, however, That if at any time the laws of this Commonwealth shall provide for the nomination of a candidate or candidates for any office or offices at non-partisan primaries, then, and in that case, every enrolled, registered or qualified elector shall be entitled to receive and vote such non-partisan primary ballot, in accordance with the provisions of the law authorizing and establishing such primary.