The events of the 20th century should put to rest that it's a good idea to take one ethnic group and select it for, or exclude it from, political power.
Eugenics, Lebensraum, the Holocaust, the two world wars of nations, the endless tribal wars of Africa all point to the superiority of having a country that makes no distinctions by race, creed or color...but it only works if the constituents of such a country agree to relate to each other on that basis.
Israel came late to the game of nations, but defined itself as Jewish, another in the long, long line of "we, and not they". Yet, inclusion and exclusion cannot be separated. Hitler choose to exclude, Israel chose to include. Neither of these has a place in the United States, that, through it's own sorry history of racism, appears to have settled the situation in favor of all-in-one with equal rights depending only on citizenship and not any sub-group identification.
This is part of the daylight that needs to exist between the U.S. and Israel. To say that America approves of a system that requires the state to decide who is a Jew is to deny the foundation of individual freedom in the lack of discrimination that we have worked so long to achieve.
Israel is a relatively fresh example of an anachronism. It is an understandable attempt by a minority to establish itself on the model of so many other nations, even as Europeans, who wrote the book on nationalism, are working for unification in various ways after having visited the abyss.
What irony to see blood and soil in Germany return as religion and soil in Israel, made up of a group that suffered enormously from the concept, now dishing out suffering to another group. But what are anti-Semitism and "Who is a Jew" if not two sides of the same coin?
The United States offers Jews, Italians, Amish, Bulgarians, Turks and everyone else who are citizens the freedom to live and worship as they wish, to speak as they wish, to dress as they wish. It allows all to build places of worship. What it doesn't offer is ancient holy sites over which to dispute ownership and holy land over which to argue priority.
Israel, though it dates as a state from 1948, is only the latest incarnation of political power in an area that has seen bloodshed for centuries past as the same sites repeatedly changed hands. It's the latest political grouping of people by religion rather than, as in the United States, by the idea of the human individual as a creature inherently worthy of dignity independent of such grouping. In this sense, the U.S. is based on a very recent concept while Israel is based on an ancient one. The founders of the United States sought to eliminate the kind exclusivity upon which Israel is based. The question of who is a Jew is only a new version of the conflict over identity which the U.S. rejects and we should have nothing to do with the idea that a religious body should sit in judgment of who may be a citizen of any country.
History tells us how this ancient idea has worked.
Because of the above, it is a non-sequitur to say there is no daylight between Israel and America.