Short story: they do not undermine the Torah, or lead to public and private policies that could undermine the Torah.
The only possible problem is that Rabbi Bar Hayim is advocating halachic positions which happen to have very few advocates today, but there is nothing inherently wrong with his positions. Further, if someone would choose to follow these positions, he would not be getting into much trouble after the fact, unlike following certain other popular opinions concerning, e.g., Sabbath and kashruth observance, or superstitions.
1. A Single Day of Rosh Hashana in Israel: Rabbi Bar Hayim claims that he is not alone in believing that this should be the correct practice. There are loads of proof it should be that way, and even was that way. Keeping Rosh Hashana one day, as the Torah intended, will not result in anyone coming closer to sinning, as the idea behind keeping two days of Rosh Hashana is not a syag, i.e., a rabbinic institution made in order to distance one from getting metaphorically close to sinning (e.g., laws against seclusion with members of the opposite sex). Doesn’t declaring the second day of Rosh Hashana not a holiday undermine the main facet of rabbinical authority, the right to decide the dates of the Jewish calendar? No, because he is restoring the holiday to the way that it was apparently established by the last authoritative Sanhedrin, the same one that promulgated our current, fixed calendar. Don’t the Rif and the Rambam disagree? Yes, but they disagree with regards to s’vara, their understanding of the relevant sources in the Talmud, but perhaps if they had been aware of the antiquity of this practice, they would have maintained it. When the students of the Rif showed up in Israel, there was barely an observant community, and when Maimonides visited he could barely find a quorum of ten men to gather for prayer.
2. Starting Shiva’ N’qiyim, the seven clean days, as soon as achieving a clean hefseq tahara: You can read the whole discussion here. Once again, aside from the fact that few advocate this opinion, which is well grounded in the sources and reality, there is nothing that can go wrong with following this practice. On the contrary: it may help many good Jews fulfill mitzwoth d’oraitha they would otherwise not be able to. I have heard many rabbis express privately that they would also encourage others to practice this way, but they somehow feel it would take a proper Sanhedrin to permit such a thing. I do not understand that claim, as it only takes a Sanhedrin to permit that which an earlier Sanhedrin prohibited, but starting n’qiyim without waiting at least four days is a practice that developed based on understandings of halachic presumptions, and therefore does not require a Sanhedrin to be removed. I was amused once when someone invoked, in all seriousness, that it would take a Sanhedrin to also re-permit men walking four cubits without a head covering, as because everyone wears a head covering, it has become a matter of strict obligation to always wear one…
3. Birkath Hahamma on the Summer Solstice, and not every 28 years in April: This is one of the few positions that I would like everyone to reconsider, and the refusal of the rabbinic establishment to address the issues raised in Rabbi Bar Hayim’s ruling is troubling, but the question only comes up once every 28 years, as the widespread custom has not changed in a millennium, and does not look like it will be changing any time soon. Widespread discussion of this issue can only increase awareness of this and other, even-more-relevant, halachoth. Even though Maimonides did describe the blessing as being recited every 28 years, according to his rules elsewhere, we should follow Rabbi Bar Hayim’s ruling. Why? Because Maimonides himself taught that it is critical to determine the proper texts of the source materials, and it has now been shown that according to the uncorrupted texts, 1. the blessing is to take place every year on the solstice and 2. Maimonides himself would rule that the blessing be recited on the solstice. I know that some argue, “well, it’s going to take more than that to force a change in halachic practice,” but to people like that, nothing is a strong enough proof.
For me, it is sufficient to note that the 28-year cycle is something the Sadducees came up with. That alone should be cause for alarm, but was nowhere to be found among all the books, articles, and posts about Birkath Hahamma the last time it came around, in April 2009.
Note that this year, the bracha should be recited on the Sabbath, June 21, 1:51 p.m. in Jerusalem, which is the precise moment of the summer solstice. Also note a historical reality that is very telling: The Talmud as we have it only mentions reciting a well-known and often-used blessing when the sun reaches it’s t’qufa, but calling this ritual “birkath hahamma” does not appear until very recently in the halachic literature. In my opinion, because the blessing “oseh maaaseh breishith” is said on the occurrence of many kinds of remarkable astronomical phenomena, like eclipses and shooting stars, then even if one were to follow the corrupted text of the Talmud and say that the sages were referring to a once-in-28-year event, one should still say this bracha on seeing the solstice. To be more exact, the three visible phenomena the day of the solstice are 1. the one I mentioned above in the middle of the day, when the arc of the sun’s path through the sky reaches its northernmost point in the year, 2. sunrise, when the sun will rise at the northernmost part of the eastern horizon, and 3. sunset, when the the sun will set at the northernmost part of the western horizon.
4. Permitting Qitniyoth: If everyone on the block can eat rice on Passover except for Goldberg, it must mean that the only problem with Goldberg’s acting like Mizrahi, Ashkenazi, and Benayun, is that he is breaking the status quo. Everything from improper Hebrew pronunciation to anti-Zionism to dressing in Polish clothing has been advocated based on this premise, a premise that has in any event been flat out rejected by many others. It is true, for example, that if one were to read the Shulhan Aruch he will find that the Beth Yosef permitted the consumption of qitniyoth on Passover while the Rema noted that the practice in Europe was not to, but one has to keep in mind that they were writing for specific communities at a specific time and in specific places. The Beth Yosef and the Rema would likely agree that centuries later, in a community composed of a population from a mixed background in a totally new settlement, like the new city of Beth El, a new communal consensus would need to be reached, and it is fairly certain that they would not take the relatively modern position of checking where each man’s paternal great grandfather was stuck in the exile. I was also wondering how rabbis on mixed battei din deal with cases between people of differing origin: do they invoke place of galuth as part of the ruling? Further, if we take into account the great grandfather’s place of origin, why do we stop in Tunisia and Poland? Why not say that both came from Israel even before that, and therefore they should be united by one stream of halacha?
Avraham Ben Yehuda 