I don't recall where I saw this before (maybe Rafi G's blog) but there is an interesting phenomenon to take note of when it comes to religious observance and Israelis. To wit, the more the government enforces a particular halacha or area of Jewish law the more non-religious Israelis struggle to break those rules. So for example the chiloni public constantly works to avoid Shabbat restrictions or find ways to eat chometz on Pesach.
On the other hand, those areas where the State chooses not to intrude show very high rates of participation among the secular population. The vast majority of Israeli males have a bris milah. Most Israeli families light Shabbos candles and make a seder every year.
This is one of the ongoing problems of having a Jewish state where the Torah is not the law of the land and the non-religious population is the large and governing majority. There is an ongoing dance between running a secular democracy and running a Jewish society. The ones doing the dance can never have a happy result. Push the secular democracy angle and the religious get upset over the diminishing Jewish nature of the society. Push the religious agenda and the seculars shout about coercion.
But perhaps the two opposite phenomena above point towards a different way, one that the Religious Zionist community might be encouraged to push for at the national level.
The ultimate goal is to turn the first flowering of our redemption into the final flowering, after all, and no way is better than by moving Israeli society towards greater observance. I would venture that most secular Israelis would welcome such a move as well if it were presented in the right away. The "you're all sinners if you're not like us!" method clearly has had little effect. Furthermore the kiruv movement works but only on a small scale and nowadays seems to barely be balancing the traffic out of observant Judaism. What we should want is a society that embraces Torah observance out of love and desire to connect to its religious and historical roots. Legal or social pressure are absolute contraindications to achieving this.
Perhaps then it's a good thing that Bayit HaYehudi is encouraging an electoral slate not exclusively composed of Religious Zionists. The old Mafdal party failed for precisely the reason that the Chareidi parties continue to succeed. Chareidi voters are sectoral, interested only in their own community's welfare so they choose the party that will best represent them whether or not such representation has a positive effect on the country as a whole. Dati Leumi voters care about the State as a whole so a party limited to their community that doesn't have a holistic platform isn't as interesting. If the Likud or Yesh Atid offer a better vision for the individual Religious Zionist then they would get the vote. Bayit Yehudi needs to avoid that trap but without losing its Dati Leumi character.
What Naftali Bennett has to do is create a system in which non-religious Jews and even non-Jewish Israelis feel that they can be part of Israeli society while maintaining that Israeli society must have an underpinning of halacha at the government level. This means proposing a government that publicly observes Shabbos and Yom Tov restrictions while granting a bit more liberty at the societal level to reduce the onerous pressure that drives people away from observance. Perhaps a balance like this will move Israeli society in the correct direction.