All three examples you cite are related to the Establishment and Free Exercise clauses of the First Amendment to the US Constitution. (Note that the 14th Amendment applies the Bill of Rights to state governments all the way down to local municipalities).

Whenever a case related to rights comes before the Supreme Court (and lower courts as well) the court has to decide how much weight to give the argument of a group or individual who claims that the First Amendment is being violated. Are they part of a suspect class, a group that has historically been discriminated against? If so then the Supreme Court applies a much stricter standard of proof (strict scrutiny) that the right should be abrogated in this particular case. If, however, the person is NOT part of a suspect class then something called rational basis scrutiny is applied instead.

Take school prayer as an example – those arguing against school prayer are usually part of a suspect class; over time Jews, Muslims, atheists, and others have argued that prayer in public school constitutes state established religion, a violation of the first clause of the First Amendment (over many years the Supreme Court has extended the clause's prohibition beyond legislation and into policy choices). In that case it is those advocating FOR prayer who have to make an argument that will hold up under strict scrutiny. Such an argument would need to prove at a level of near perfection that the state interest in holding prayers is so strong that it supersedes the establishment clause. BTW, the situation you cite is protest, not law, so I am not sure how it applies here.

The peyote case demonstrates how suspect class does not automatically mean that a member of the class will win – since the law in question prohibited the use of illegal substances and was not a banning specifically of religious practice it did not violate the Free Exercise clause. "Oregon's ban on the possession of peyote is not a law specifically aimed at a physical act engaged in for a religious reason." Since the law applies the same to everyone AND the state could make a compelling case that there was a state interest the men were denied their unemployment benefits – BTW, they were fired from a DRUG REHABILITATION CLINIC for their use of peyote, and were trying to use the First Amendment argument to collect benefits by saying they were fired without cause.

NYC's debate about circumcisions should not apply here because no laws have been made or applied.

In any case, the difference between Israel and the USA is that while Israel has a right of Free Exercise it does NOT have an Establishment cause. Judaism is the state established and supported religion of the state of Israel. That is why your school prayer example does not work here since the challenges to those prayers are based on the Establishment Clause. As for the peyote case, the core question remains whether the authorities can make a compelling argument that there is a state interest in keeping women (and egalitarian groups, and people who want to use guitars on Shabbat, etc) from praying at the Kotel while engaging in rituals that have been deemed unacceptable and even offensive by many of the Jews who pray there as well.

It is also worth noting that this essay completely ignores the recent court ruling in Israel that found the law you mentioned does NOT prevent women from wearing tallit and tefillin, reading from the Torah, etc. That is why today the Israeli police were protecting WoW instead of arresting them.

Israel still has to answer the following: Is there a compelling state interest in restricting religious practice at the Kotel to a very specific range based on (basically) Haredi and normative Orthodox practices? I don't think there is.

P.S. In general I often wonder… how can one demand his/her arguments to be taken seriously if he/she does not respect them to start with, as demonstrated with an unwillingness to express them properly, unencumbered by poor use of grammar and bad spelling, or by the lack of care to address the other with the most basic courtesy expected in a civilised conversation?