Devotees who rely on observation in Israel of the Abib barley in the spring to commence a new year, and on observations of the new moon in Israel to declare a new month, inherently must make interpretations and inferences (dare I say traditions) of their own in order to come up with the answer, so who is to say their assumptions are any better than the "traditions of men" they seek to supplant? Who is to say their leaders are qualified to make such pronouncements? These are just some of my thoughts. Now to the post, slightly edited from the original to expand and clarify as possible. This is many-sided topic that I would like to return to. This post is just a start.
Yeshua was most certainly voluntarily subject to various dictates of His culture. He acknowledged the corrupt Zaddokim priesthood, and declared that the P'rsuhim sit in Moses seat, therefore do as they tell you, but do not do according to their works (Matthew 23:2-3, for discussion of Nehemiah Gordon's questionable hypothesis on this verse based on Shem Tov, see this article). It appears that the example and instruction that we have is that whether or not they accepted or acknowledged Yeshua, the scribes and P'rushim retained a measure of authority for Yeshua's disciples, therefore we cannot glibly dismiss the teaching and understanding of the Sages. Don't misread that: I don't believe today's rabbis represent halachic authority for any who follow Yeshua. He is our halachic authority, and as His disciples we are to walk in the same steps that he walked. Yeshua was not unnecessarily antagonistic against the P'rushim and fought them with respect to weightier matters where their tradition clearly set aside the commandment of God, leading to sin. He was not confined by their innovations, but didn't fill his time of teaching with ceaseless nit-picking or wholesale rejection of their halachah. He recognized their authority, in the same way that David was able to submit to Saul's authority, realizing that so doing was pleasing to His Father, and that the P'rushim exercised no authority that they had not already been granted by Him. He is our example.
It is beyond amazing that people are recognizing the biblical lunar calendar and observing the biblical feasts as Messiah and the apostles practiced and taught, ALONGSIDE the unbelieving Jews. Yeshua went to Jerusalem when the feast was declared, and didn't spend his whole time elucidating on conjunctions and crescents like an astrologer. He had more important things on His mind. I think we should eschew the Gregorian new year, but to proceed further as some suggest, and to refuse to observe the biblical calendar with the Jewish people who have carried it forward against great tribulation, and insert our own fledgling understanding of the biblical calendar in its place, would appear to be presumption and arrogance against the natural branches (Romans 11:17-18).
Let us be humble and prepare to learn over long periods of time instead of needling unbelieving and messianic Jews about stages of barley and the phases of the moon. The discovery is not new by any means, nor does it grant any particular distinction to its adherents. It is a priestly function to declare the months and feasts (Numbers 10:8-10), and to my knowledge there is no temple and no ordained priesthood. For teachers to take it upon themselves to declare the start of the months and years based on a limited understanding and almost no mandate is presumptuous, begging the same retribution that Korah, Dathan, and Abiram met with when desiring to make themselves priests (Numbers 16, esp. v. 10).
It assumes that one is dead right about their reckoning of the new moon and abib barley and that everyone else, even thousands of years of the most exacting scholarship, is dead wrong. It is a speculative matter, at best, and there is nothing redeeming about the disunity and exclusion that the moon-watchers foment, there is no end to it, even among themselves. Is it first-crescent, three stars after sunset? Is it a day in-between last and first crescent, when the moon is completely dark? Is it only as observed from Israel, or can it be observed and declared in one's locality? And so one sees how there is much dissonance and strife even within a very small thing. Think what you think, practice it, and evaluate the fruit in the context of the whole.
The good news is: Yeshua, Messiah of Israel, crucified and resurrected. Not: did you know that every Jew since I don't know when has been celebrating the biblical feasts *a few days* (or possibly, one month) off and boy, we really gotta fix that or we're all doomed (this would be an appropriate launch point for a discussion on the eschatology of the fall feasts, but for a different day). I understand that the astronomical calculations and associated rules may be imperfect, but they served an important purpose after the destruction of the temple when Jews were scattered and unable to celebrate in unity using the more ancient ways of communicating the new month in a timely matter. The internet makes it technically possible to consider doing something different, but until a true Sanhedrin and ordained priesthood is restored that can proclaim the months and feasts, in harmony, any attempt to "restore" the exact timing of each month is divisive, presumptuous, and exclusive, not advancing the message of the kingdom of Yeshua.

Now here's where my launching pad for most of the below is. There are some who push things farther than simply observing the Jewish biblical calendar and reject the astronomical calculations used to determine new moons and deciding whether to intercalate (that is, add a month) in a given year, and choose instead to mark time by observations made in the land of Israel. On the surface, this seems reasonable and even revolutionary. At the most basic level, the issue is not whether to observe a biblical calendar, but how one should decide whether a given lunar month should have 29 or 3o days and whether a biblical year should have 12 or 13 months.