1. “religious matters” was defined vary narrowly to exclude any involvement by Orthodox Jews in public affairs. Remember that in the first elections, Ben Gurion’s principal opponents were parties on the left (who advocated banning yeshivos and changing the day of rest, among other things). If you are in to alternative history, consider what if Ben Gurion lost (e.g. Israel as a member of Comecon and the Warsaw Pact).
2. In part because they believed their own propaganda, it was assumed that in a generation there would be so few Orthodox Jews left that it would be no problem to wait and then get to work on closing yeshivos, conscripting all frum children, and realizing the long term zionist dream of being an “Am Hofshi” (secular state, free from the yoke of Torah). It took awhile before it dawned on them that the socialist revolution would end up in the dustbin of history.