Sam2 and coffee addict,
They could drive on shabbos without batting an eyelash and still call themselves orthodox, at least reform an conservative changed their name
ca: Nah. They’ve been more “halachic” than that so far. I don’t see that coming.
Driving on Shabbos was a big issue for the conservative movement, because the vast majority of its adherents were suburbanites who did not cluster around synagogues. Note that the ruling permitting driving on Shabbos came in the 1950s, but counting women as part of a minyan did not start until the 1970s, and the first conservative female rabbi was ordained in the mid 1980s.
Open Orthodoxy at this point seems most active in more urban areas, where walking to synagogue is more feasible (and as an aside, in line with environmental activism), so that is not where the pressure to change is coming from. So I agree with Sam2 that we are not likely to see a blanket permission to drive on Shabbos ruling from the Open Orthodox movement in the near future.