Please point out where in the Constitution it says that assimilating to YOUR particular norms is a condition of achieving citizenship.
You say "abide by our rules and laws" - check.
How does wearing a burqa, practicing the Muslim religion, and not mingling in society violate our laws? And how is this not "assimilating" when the foundation for our laws - the Bill of Rights - explicitly grants the free practice of religion? Do you not recall that the entire point of the European migration to America was to come to a place where one could practice a non-state sanctioned religion and that this is a FUNDAMENTAL value incorporated into the Constitution?
If YOU don't like that fact that this woman, so long as she wishes to abide by our laws as established by the Constitution, can and *should* become a U.S. citizen, regardless of how well you think she has "assimilated", then it is YOU that has the cultural problem. If you can't be comfortable with her practicing her individual freedoms, then perhaps YOU should find a country where it's a requirement that everybody wishing to be a citizen "fit in". France sounds like a good choice.
Abiding by our rules and laws means an obstinate, burqa wearing, devout Muslim, who wishes to not leave her house CAN be a citizen. If you aren't OK with this, then YOU haven't assimilated to American values and you should leave. Simple.