Once upon a time it was the Arabs that were going to take over society. This fear has eased somewhat since the Oslo Discords, in about the only way they helped Israel, created a sort of Palestinian citizenship which means the vast majority of Arabs living in Yesha are unlikely to show up in Israel tomorrow demanding citizenship there. As for the Arab minority in Israel, despite prodigious fecundity it seems to remain at 20% of the total population over time.
So the real threat nowadays, according to the pundits, is the Chareidi community. Chareidim, with a proclivity for children that makes Arab women look barren, are exploding in terms of population size. Given that the average secular Israeli has about 2 kids or less, this means that some time in the next few decades the Chareidi population will reach a percentage of the population that gives them enough votes to control the Knesset and install a Chareidi government.
Personally, I don't think this will happen for a long time for a couple of reasons. One, the fear of growth of the Chareidi population is probably overstated. As too many blogs out there are happy to point out the tide of baalei teshuvah is more than amply matched by the opposite current creating chozrei b'she'elah. What's more, keep in mind that Chareidim are just as Jewish as the rest of us. The Chareidi community is not some monolithic entity with a tight oligarchal committee of elders controlled their every move. It is just as fractious as general Jewish society and with size will come more division. There are already three Chareidi parties in the Knesset and over time it's not hard to believe that the United Torah Judaism merge of the former Chasidic and Misnagdic parties will once again split. Yes, one might imagine a Chareidi coalition one day but more likely there will be enough infighting to prevent a workable one from arising.
Nevertheless we must consider that one day there will be a Chareidi government. The next question, then, is: what would such a government look like? Over on his blog, Professor Marc Shapiro, normally a calm writer, waves very eloquently in an alarmist fashion over the possibility.
Now I would certainly not presume to debate with some of Prof. Shapiro's points. A future Chareidi government would take its orders from "the Gedolim" and those "Gedolim" are carefully isolated from their own societies and routinely fed misinformation by their handlers who then take their pronouncements (assuming the handlers didn't make those us on their own anyway) and declare them to be "Daas Torah" for the masses.
To begin with, if haredim were ever the majority, funding for non-Orthodox (and perhaps even Religious Zionist/Modern Orthodox) schools would be halted. There would be massive decreases of funding for universities, with the humanities taking the biggest cuts, and money for the arts, culture, and institutions connected to Zionism would dry up. Freedom of the press would be abolished, artistic freedoms would be curbed, and organ transplants would almost entirely vanish. Public Shabbat observance and separate-sex public transportation would likely be required. There would also be restrictions on what forms of public entertainment and media are permissible and on public roles for women. Of course, women’s sporting events would no longer be televised and men would not be permitted to attend them.But despite their massive dislike for democracy and their refusal to grant legitimacy in any area other than the Chareidi one they would be unlikely to be successful in many of these endeavors. For one thing, Israel has a very strong and independent Supreme Court that makes it its business to ensure the State is as secular as possible. The morning after a Chareidi government came into being, that Supreme Court would still be there. Any attempts to alter laws that involved infringing on the secular rights already taken as givens in Israel today would be shot down. Unlike Iran and Saudi Arabia, the ruling "Gedolim" do not also control the justices and they would certainly fight back against attempts to turn Israel into a theologically fascist state.
What's more, Chareidi might be fanatic but they are not stupid. They would well realize that an attempt to kill the "golden goose" that Israel has become for them would result in the destruction, chas v'shalom, not only of Israel but of the majority of their community. After all, what kind of shape will Israel be in as hundreds of thousands of chilonim and their money flee the country to avoid living in a kosher Iran?
All in all it's okay to wonder "Hey what would things be like if those guys too over" and the shudder at the thought but I don't think it's going to happen in our lifetimes or the next.