To me it all comes back to the issue of the item of clothing preventing her from doing her job effectively. A teachers job is
communication, and the veil was (allegedly) preventing effective communication with her pupils.
I wouldn't want a surgeon operating on my brain while wearing a nice pair of sheepskin mitts, or to be rescued from a burning building by a fireman in high heels. You could equally argue that either of those "shouldn't be told what to wear", but the fact is that a great many of us have to make concessions when entering the workplace.
Although I suppose a less flippant parallel would be the Sikh's turban.
Wikipedia wrote:For Sikhs, the use of turban excludes the wearing of a cap. In India, Sikh riders of motorcycles are exempt from wearing crash helmets. Similarly, a Sikh soldier would not wear a steel helmet even under shelling or firing. However, in some foreign countries the compulsion of wearing a turban, like the wearing of long, untrimmed hair, has sometimes led to the Sikhs being placed in a position of conflict with employers or even governments whose rules or laws require the wearing of a cap or helmet.
The turban being religiously obligatory for the Sikhs, a more tolerant view has begun to be taken recently. For example, the Motor Cycle Crash Helmets (Religious Exemption) Act passed in British Parliament in 1976 exempts “any follower of the Sikh religion while he is wearing a turban� from having to wear a crash helmet. Similarly, the highest court of the country in the United Kingdom, the House of Lords, has ruled that Sikh drivers and conductors of public vehicles are not to be compelled to wear caps. Similarly in Canada in 1986 Sikhs in the Metro Toronto Police were granted the right to wear turbans rather than caps while on duty, and since 1990 have been able to wear their turban while serving in the Royal Canadian Mounted Police.
A very interesting news article from a couple of years ago
here, contrasting somewhat with the current face veil case.