OP, what makes you think that Lapid is such an extreme change?
There have always been some aspects of halacha in the Israeli government, and there still are. Sometimes it was more, sometimes it was less.
Some halacha does not equal Judaism. Refrom believes in some halacha but it’s not Judaism at all. Kefira in one letter of תורה שבכתב or תורה שבעל פה is kefira in the entire Torah.
Of course, this is not speaking about people, rather institutions. If a rabbi says lashon harah once, he is still a rabbi. If he announces that the halachos of lashon harah don’t apply anymore – he is a kofer in the entire Torah and no longer represents Judaism.
The “State of Israel” never supported the entire Torah, so it was never a “Jewish State”.
Of course, as Jews, we try to influence them to have as much halacha as possible, since this affects millions of Jews.