"Faith" is a big word, but for many/most haredi people "community" is the more operative term. Leaving a sect means becoming an outsider. All their family and friend relationships are insider-based. Regardless of the severity of luteral shunning practices, the nature or haredi lifestyle makes these aspects severe regardless. There's a lot of variance between communities though.
In any case, people do leave. Often, it's relatively early in life. This is why haredi communities are so leery of military service, college lifestyles and such.
People also join. A lot of Chabad adjacent communities are largely converts and 2nd generation members.
I would also emphasize that lifestyle, community, belonging, mission and such tend to play as big a role as belief in convincing converts.
Judaism doesn't always emphasize belief in its definition of "faith." At least, far less than Christianity and Islam. This a philosophical tradition going way back. Faithfulness and even spirituality are often seen as concerning practice (ritual, but also moral) moreso than concerning faith.
Belief follows practice, and if it doesn't... at least you have practice. The Christian Brothers pinched this line from an old rabbi.
Faith isn't quite the right word for what I mean, but community isn't either. The particular set of opinions or practices that have the practical effect of keeping the parents (and some grown-up children) separated from the wider society. (The concrete practical effect mentioned upthread was being vaccinated.)
They succeed in part by insulating their children from Western culture (no TV, no Internet, little interaction with outsiders), and by giving them very little in terms of secular education, so that getting a career is not really an option for most.
Unfortunately, for the ultra orthodox, yes. The parliamentary system is a majority coalition, and more often than not, the ultra orthodox parties are the kingmakers, so they get a lot more influence than one would expect.
Specifically, they are exempt from the standard Israeli STEM + foreign language curriculum (which is quite comprehensive - to graduate highschool, you need passing grades in standardized tests that includes -- among other things -- English, Math, at least one of biology/physics/chemistry, literature, history, Hebrew, sometimes bible studies -- depends on the government at the time). You have to have 20 credits among these - at least 3 in English, at least 3 in Math, and there are more requirements).
About 10 years ago, there was a government they were not part of, and this exemption was removed ; but the following cycle, they were kingmakers again and it got reinstated.
Edit: Added some details about the Israeli curriculum.
