Either burkas and full-face veils are essentially (and only) expressions of religious piety, or they essentially differ from other religious head coverings by symbolically (or actually) removing women from public life.
Martha Nussbaum adopts the first assumption; in a response to her piece, Feisal Mohamed defends the latter.
The adoption of burka bans in European cities and countries is a new development, but the essentials of this debate are not. Susan Moller Okin's excellent "Is Multiculturalism Bad for Women?," though 10 years old, is still relevant. Her title essay is followed by a number of responses, including one by Nussbaum broadly defending expression of religious freedom.
As Mohamed points out in his commentary, the key issue is not whether to support religious freedom (there is broad agreement--outside of the French public schools anyway--that religious dress is not in itself at odds with multicultural, liberal society). The key issue is how to assess conflicts between religious demands and individual and group rights to autonomy.
This reduces a theoretical question to a practical one: for women who are covered to a point that participation in civic life as individuals becomes difficult or impossible (or as a symbol of their non-participation in public life), what policy is most likely to reduce oppression? As a matter of practical results, it's not clear to me that a burka ban would actually result in those women being fully engaged in public, educational, and civic life. Instead, they might become even more cloistered than before.
This has been a fruitful topic for discussion in my feminist theory course, and now that it's prominent in the news, I would consider integrating it into a topically oriented intro to philosophy course. Comments welcome on how you think this topic would be received by a lower-level audience.