From someone who actually interacts with non-religious people, I can assure you that making Sunday another day off will merely increase their weekend chilul of Shabbat and not prevent. They will still open their stores, they will still tour the country. It is human nature, even overseas, North American and Europe could not prevent keeping stores open on Sunday.Bayit Yehudi - register this as: Fail.Josh
First, there are places in the US where stores are closed on Sunday by law. Second, as someone who also interacts with non-religious people, I think a number are traditional enough that they would not drive and do fewer melachot if it was not the only day off. Further, as Bennett likely knows, there are a number of mixed religious/non-religious marriages in which having shabbat the only day to take off and visit family etc. is a big problem and causes much tension in the marriage. speak to someone in such a relationship and ask them how much Sunday off would benefit them.