People should be free to wear whatever they want. But that being said, I believe the burqa to be detrimental to the individual as well as society as a whole. I live in a country where trust and cooperation are paramount. This poses two undeniable problems:
1. It is difficult to trust someone whose face is obscured. Interacting with someone whose face is obscured is unnerving. You need to be able to see and identify who you're talking to as well as read their facial expressions for signs of their emotions, intentions etc. These are important non-verbal hints when humans communicate with each other.
2. As an extension of #1, wearing a burqa makes you practically unemployable. Most potentiel coworkers will have a hard time forming any kind of bond with someone that they've never really seen. In addition, few people who grew up in a free and open society will feel comfortable doing business with a completely anonymous stranger that's hidden away under a pile of cloth.
If you artificially limit yourself from being part of the workforce you're not contributing to society and that's a big problem. We all have a responsibility to strive for self-sustainability. Choosing to place yourself outside the workforce leaves you with few options. Women who choose to wear a burqa could theoretically have someone, like a husband, provide for them but more often than not they'll apply for unemployment benefits. This constitutes an unreasonable drain on taxpayer resources.
Again, I believe, on principle, that legislating against wearing the burqa is wrong. However, it is a general rule that you must make yourself available to the labor market if you are to receive unemployment benefits. Hence, if you deliberately make yourself unemployable, you shouldn't be eligible to receive benefits.
You may call me a cynic, but I'll venture a prediction: If eligibility to receive financial support from the state was made consistently (meaning for both Frederikke and Fatima) contingent upon your actual availability to the labor market, thus precluding the wearing of a burqa, we'd see "sincerely held religious beliefs" disappear in a matter of minutes and Fatima would be walking around in a pair of jeans before the end of the day.