Sarah, which MO rabbis have put in writing that married women are not required to cover? I was only aware of R’ Broyde’s essay tentatively proposing the potential basis for a heter but not actually paskening that it’s not required.
A rav privately telling a married women not to cover her hair for shalom bayis reasons does not mean it’s not required. When you’re dealing with shalom bayis and especially the issue of married couples when one but not the other is becoming a ba’al teshuvah, leniencies on all kinds of issues (Torah or rabbinic) abound. This is because as a practical matter, if a new BT who had already been married to a chiloni demands to follow all the mitzvos 100% right away, the marriage is over, while if they take things slowly and play their cards right, they can become completely observant by waiting patiently for their spouse to get on board when they’re ready.
Right before a ger finishes their gerus, they are asked if they accept as binding on themselves all the mitzvos, or the entire Torah without reservation, or some such language. If they say yes and mean it, as a normal sincere ger will (and they’re not really thinking at that precise moment, “No, I don’t accept them all, I just accept the mitzvos that people in my community normally follow” or “I don’t really believe in this stuff, I’m just doing this to fit in with the community or get married” or “I only accept those mitzvos I personally believe in” or “I accept all the mitzvos but that one I don’t like”), then the gerus is valid even if they are not 100% observant right after they emerge from the mikvah.
It is possible to accept all the mitzvos as binding without doing them right after the gerus. How do I know this? Because that’s the way gerus was always done in the past! They were taught a little, about a small handful of mitzvos, and then they converted and became observant afterward.
If a ger converted while being confused about what is required and what isn’t (like with headcoverings or whatever), again no problem, as long as they had the sincere general intent to accept all the mitzvos as binding upon themselves.
Of course, normally a ger today should be completely observant after gerus, and if they aren’t it reasonably raises doubts about their intent at the time of gerus. But if for some reason he’s not 100% observant right after gerus for whatever reason, like lack of willpower, lack of knowledge, confusion about what’s required, conforming to the community or spouse or whatever, then that’s unfortunate and wrong (he should have the guts and responsibility to find out what’s required and do it!), but as long as he sincerely accepted all the mitzvos as binding upon himself right before gerus, then his gerus is still valid. Accepting the yoke of the mitzvos doesn’t mean that you commit never to do a single aveira in your entire life — it just means you accept all the mitzvos as binding on you just as they are binding on any born Jew.
You might ask, then why aren’t Conservative gerim valid? As Avi K implied, the main reason is that the rabbis are actually apikorsim and thus are not kosher witnesses.