I believe some of the division, confusion and upset is the vast difference between what is perceived as the Messianic movement in North America vs elsewhere, and how we came to be as a whole in the Americas being the bulk of the disagreement. Not "One Law", "Divine Invitation", "Two House" or any of the other smaller doctrinal differences... or even the different "umbrellas" of MJ.
Yesterday, while watching a history-related documentary about the Prohibition some of this discussion came to mind. Some of the very issues we're wrestling back and forth with, are the core issues that only are seen/handled in US congregations and the vastly different flavor we have from the rest of the world due to not only our world view, but the fact of where many of the congregations were began. Between the various Methodist, Baptist, Assemblies of G-d, Presbyterian and Catholic congregations that later encorporated Messianic services, or umbrella congregations, we have ethics, doctrines and dogma tagging along for the ride. This could be the difference between one's understanding of or allowance for liturgy, wine, more Jewish practice, mode of baptism and views on salvation/obedience/works. This would also mean a different understanding of involvement in the public/government sector as far as legislating morality.
Then you have also those "we're on our own" home group types that have a mishmash of everything up above...
Here in Europe and elsewhere, you find that the movement seems to be a little more solidified... not as many doctrinal differences, though different modes of worship, levels of kashrut, and percentage of Jew and Gentile worshiping together.
I have no problems meeting with someone from the MJAA, UCMJ or MIA or any other group. I find that at the core, we truly believe many of the same things. It's in practice, and some other doctrinal issues where we have some of the split hairs. Personally, I believe in two house, but not like the MIA teaches. I gain benefit from some of their teachers, but not all. I find benefit from both major camps of the MJ movement, but not in some avenues. I find major issue with the whole of the "Karaite" Messianic groups, and that I can't seem to get along with any of them because the issue of rabbinic authority always comes up, and they're right, we're wrong. I just get tired of it and move on.
Having been purchasing Messianic books as of late, I am finding a lot of the theology and doctrine being pushed is more like what I heard growing up, than what I had been hearing from either Messianic camp as of late, whether online, or in audio/video format & in person.
Some of it has to do with the temperance movement, some of it has to do with WASP-type beliefs. It tends to be broken down some as to whichever congregation the MJ core group came out of or is sponsored by. Which is why in many groups, you find basic Baptist beliefs, including pre tribulational rapture, pre-wrath, anti-liturgy/anti-tradition (other than Baptist), anti-Judaism, dispensational, covenental, Calvanistic (
Three,
four and
five point) theology, OSAS/OSNAS... There's a range between SBC and IBC thought in that group. - then you have those coming out of the Methodist groups, which tend to lean more Arminian (though sometimes leaning more Calvanist), traditionalist, holding to sacremental theology and also liturgy - open (though not always) to the ideas and avenues of Rabbinic thought as it relates to practice of MJ.
My experience with Hebrew Catholics has been limited, but those I have known equally hold Messianic Beliefs along with tenants of Catholicism and see no difference or "split" in the two belief systems. One friend kept wholly kosher to the 9s, while the other disagreed on the concept of cheese and meat - not sure if that was due to his Sephardic stint on things or not.
Where I was going with the issue brought forward about the Prohibition - is that most the congregations born out of the WASP group, tend to believe in the morality of legislating morality, pushing political leanings and thoughts from the pulpit or classroom, and if you aren't of their leaning, somehow something's wrong with you or you're less American or less religious or "whatever".

That everything's cut and dry, white and black - no shades of gray.. Using the term "biblical" is really meaning "Our understanding of what is Biblical based on our understanding of the KJV 1611 AV and our doctrine and dogma - if you believe differently than us, you're a heretic." The whole "only we are the true church, everyone else is in hell" -- the classic jokes about how you'll see one denomination in the liquor store, and the other one will be only coming in at hours no one who knows them will see them purchasing... Heavy on outreach to non-WASP groups, to "save them from their cultural ills" - that kind of thing.