I can’t speak about the haredi man on the street, but examination of the writings of the haredi leadership – and in the haredi world that is what really matters – shows that time and again they have expressed opposition to democratic values as well as democracy as a governmental system.
From the haredi leadership’s perspective, while at the present time the haredi world is forced to take part in the democratic process, they assume that if haredim ever became a majority they would dismantle Israel’s democracy and institute a Torah state (i.e., a theocracy led by the haredi gedolim). Since that is their goal, stated explicitly, we have to wonder what such a society would look like. 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.