Dear Avira,
There you go again! Equating shuls with davening……
Now to be a bit serious, your talking about a halachic system. Anybody who can learn, (Conservative, Reform, or even Athiest.) is aware of the systems running throughout our Torah. The supposed schism is how much weight does the individual Chacham’s understanding have on the system versus the context that gives that understanding. And after several tries, there is no apparent answer. So while maybe if we think hard enough we can come up with a clear response, it is very likely that this has nothing to do with the break that actually occurred in the past century. I’m not assuming that Conservative and Orthodoxy are only different associations and nothing else. But it is clear to me, that it is not about something that could ever be debated.