As for the attitude towards the State of Israel, my understanding is that religious Jews generally support it, except for an ultra-Orthodox fringe who believe that Zionism is an irreverent mockery...

This is a good (even the best) first step in the process of going from confusion to knowledge, but it's mostly wrong, somewhat less enlightening than replacing the concept of a banana with the concept of molecules, while ignoring atoms and quarks.

"Support [Israel]" doesn't mean only one thing without more context, even in most people's minds, any more than "like people" would if I asked if you "like people". About half the self-identifying Orthodox Jews in Israel and far fewer than that in America do not find any religious justification or basis for the modern state of Israel and are the Chareidim. This includes almost all Chasidim. Worse than not finding warrant for it, there is Talmudic justification for opposing its creation, while reactions to finding it created predictably differ.

The most noticeable members of this group are the dozen or hundred or so portion of the Neturei Karta who spend a lot of time and effort seeking to replace the state with another state, any other state, even an Arab one, at any cost. They are better known in the West than influential or representative people for the same reason an Afghan might be more likely to know about the Westboro Baptist Church than the Anglicans.

The reaction of most Chareidi Jews to the state is more similar to their reaction to most things without scriptural warrant, such as glasses or air conditioning, i.e. little concern. At least, it would likely be so, if not for a few other important factors.

Sticking with religious issues for now, it is a largely secular state. It is not obvious how religious or coercive any religious person should want their government, but it's easy to see why autocratically minded theocrats could reach a (deceptively unanimous) consensus that the current state isn't religious enough, details aside. This widespread opinion is a theoretically defeasible concern, unlike the narrowly-held pure religious opposition to any non-Messianic state.

The next issue is a social reaction to the rest of the Jewish world, particularly the Religious Zionists but more broadly the Modern Orthodox in general. Religious Zionists find that the current state meets their religious criteria to deserve their full backing. This position is more popular among the less religiously extreme. Reaching it requires a more expedient and flexible reading of religious texts and understanding of what the tradition entails. The conclusion that Israel is A-OK is what the judge should feel in his heart before inquiring into the religious texts. To quote Barack Obama, "We need somebody who's got the heart, the empathy, to recognize what it's like to be a young teenage mom, the empathy to understand what it's like to be poor or African-American or gay or disabled or old - and that's the criterion by which I'll be selecting my judges." It is no coincidence that the "living constitution" branch of Judaism that decided to go along with what the other Jews were doing had previously decided that it wasn't necessary to wear fur hats in the summer.

The identification of the secular state of Israel as religiously significant is regarded by Chareidim as akin to idol worship, a reductio ad absurdum of deciding what the tradition says before examining it, and it is to Religious Zionism that the Chareidim are opposed, along with their opposition to the domestic policies of the state.

It is these less extreme religious Jews who are the "settlers", attempting to graft biblical injunctions of foreign policy to Israel. Interpretations of these vary widely, perhaps the most widespread interpretation absolutely forbids surrendering territory but is very lenient and practical regarding how hard one must try to conquer all of the designated land. Relatively fewer of these live in America, as they see it as necessary to dwell in the state, particularly where it advances Israel's strategic interests.

Less literal and more liberal Jews who are still Orthodox are more likely to have a standard set of liberal positions, including regarding Israel and church-state separation.

It is in one sense very unfair to call extremists more religious than non-extremists. Many self-identifying Orthodox Jews might even assert and/or believe that the greatest rabbis of the other camps are more religious than they are, even for less extreme camps. In another sense, it is of course quite fair.

So we see the flexibility of interpretation has led to the centrists being the most irredentist, a position one expects to find religious extremists occupying. It is generally false that the extremists compensate by having logically irreconcilable differences with the state, though this notion can be forgiven since the most visible do and the rest have practically irreconcilable differences with the state as it is.

Demographically, Chareidim in America are less extreme than those in Israel, particularly among the non-Chassidim. Religious Zionists are far fewer, and the Modern Orthodox form a solid continuum from Religious Zionists to the secular American left. The mainstream Israeli left is probably to the right of the American left's statements, though perhaps not to its actions, if you consider Obama representative or if you think important the left's non-response to Guantanamo staying open, drone strikes in Pakistan continuing, undeclared action in Libya, etc. American non-Chassidic Chareidim are somewhat more pro-Israel than one would expect from the extent to which they are less extreme than Israeli non-Chassidic Chareidim, and are probably less cheated by conflation with Chrisitian fundamentalists than any other Jewish group regarding their beliefs and degree of nationalism.

Sephardim never collectively went through the shock of the enlightenment and have more traditional social forces, such as social cohesion around place of origin rather than level of observance and extended families with all levels of observance represented. Even the less religious are generally unlikely to see Reform or Conservative as at all valid and consider Judaism as degrees of Orthodoxy, and Israeli Ashkenazim are similar in this respect. Sephardim generally have little sympathy for active anti--Zionism and behave more like liberal somewhat nationalistic Modern Orthodox Jews with mildly Religious Zionist Rabbis, the top leaders of whom are actually mildly anti-Zionist and confederate with Chareidim.

This is all intended to be an enlightenment for those who know only of bananas as fruit, in which I explain bananas are made of little bricks called molecules. If anyone wants to correct or add anything, or take this as a starting point for explaining how bananas are really made of quarks (but first we really must teach you atoms as if they were billiard balls...) feel free. This isn't the type of thing I have done any formal study of but it's the type of thing one develops a perspective on, however biased, and I find that regarding this topic there is so much confusion that I think reading this will help many.

Lessdazed gave what seems to me to be a good answer to most of these questions so I'll just address the remaining one (which unfortunately is one of the one's I don't know as much about.)

In particular, in many countries there is the institution of "Chief Rabbi" that enjoys some government recognition, but which Jewish groups stand behind those?

The Chief Rabbi as a separate institution evolved when in the late Middle Ages the various European states wanted official representatives of the Jewish population to talk to the government. Since for many purposes Jews were often autonomous groups this was the primary method of interaction. Somewhat similarly, in some places such as England, all recognized religions had to have a recognized chief clergy member who was actually considered to serve the monarch. For essentially historical reasons, this job has been generally taken up by a prominent Orthodox Rabbi in most countries where the title exists. In some countries with small Jewish populations (such as Norway and New Zealand) there's very rarely more than one Orthodox Rabbi and so this individual becomes the Chief Rabbi more or less by default. In countries with larger Jewish communities this position can be surrounded by heavy politics and other considerations. Also in some countries the Chief Rabbi is not actually a government recognized position but is the term used to refer to a certain position overseeing some large organization of shulls.

I object to your use of "a priori". I am aware of ironclad arguments that it is incorrect to dislike and fear certain groups. These arguments are not fully general - they do not apply to all groups.

Is it obvious to you that these cases are symmetrical? It is not obvious to me.

I never claimed to be unbiased. I, in fact, went out of the way to state a lack of confidence in my local rationality.

I would like to "flag" this post as the point where "experienc[ing] fear and hostility" was warped into "feeling fear and hostility towards". That makes comments below subject to equivocation. It does not mean anything, at least not any one thing, to "[feel] fear and hostility towards" anything. The fear and hostility are in the brain and do not emanate therefrom.

This is more than a semantic quibble. Consider the fallacy of composition. It is possible for a liberal to hate all poor people and love the poor, and for a Confederate soldier to have hated blacks and loved all blacks.

I don't think "dislike and fear certain groups" is precise enough to have an non-careful conversation about because it is more than one thing.

Ok, but that's mostly because you use that particular cutoff point, European decended populations just have gone through the demographic transition earlier and their share of world population is similar to what it was in 1750. It has nothing to do with any selection against blue eyes in the usual sense.