Although there may be a wide range of Open Orthodox shuls, may one daven in an Open Orthodox shul if a woman leads as the chazan for shacharis or ba'al koreh? Would such an Open Orthodox shul have the same halachic status as Conservative, which Rav Moshe Igros Moshe (EH 2:17) forbade davening inside? What about merely entering for a bar mitzvah without davening?
Your description of what "Open Orthodoxy" does means that it is no different from the Conservative movement. You have stated that the baal koreh or baal tefilah can be women. As Rabbi Avi Shafran explains in Denominational Déjà Vu the movement appears to be on the same path that the "Conservative" movement has already traveled.
As a result, the halacha would appear to be the same as the original psak on that movement (even before it reached its current status).
I perceive precisely the same Conservative approach to halacha in what bills itself today as “Open Orthodoxy.”
Whether the halachic topic being addressed is same-sex relationships, interfaith interactions, kashrut, marriage, divorce or conversion, the desideratum of “Open Orthodoxy” is unmistakably to bring Jewish religious praxis “into line” with contemporary mores. That may not be explicit in the wording of “Open Orthodox” statements or responsa — any more than it was 14 years ago in those of the Conservative movement. But in both cases it is manifest.
Let me stress that I am speaking of a concept here, not people; of theological systems, not the intentions of students who have been attracted to “Open Orthodox” institutions, some of whom are clearly idealists who wish to serve the Jewish people. The problem isn’t those students or their idealism, but rather the proposition they are taught, that halacha is ripe for “updating.”
The new movement’s name is a misnomer, a dangerously misleading one. Just as “kosher-style” food isn’t kosher, neither is “Open Orthodoxy” Orthodox. It is neo-Conservatism. Which is why the greatest, most widely recognized, Torah scholars today — and not only those of the charedi world — have rejected its Jewish authenticity.
I take no pleasure in revealing the truth about “Open Orthodoxy.” But truth-in-labeling is not only a civil mandate but a halachic one.