Face-veiling is customary, not religious.
The Quran tells women that they must dress modestly. However, this is open to interpretation. There is nothing in the Islamic faith that makes wearing a burka obligatory and many opt not to, instead wearing a niqab (which leaves the eyes visible), a chador or a hijab.
If it is not obligatory to wear a burka, then there is nothing wrong with banning the burka. It would be akin to banning cannabis or riding a motorcycle without a helmet. It is an optional custom that some people choose to engage in which can have a detrimental effect on integration, gender equality and national security. Women who wear the burka can wear a niqab, hijab, chador, shayla, al-Amira or khimar instead. There would be minimal disruption to their lives and it would not hinder their freedom to practice their religion in accordance with their sacred scripture.
The burden of proof lies on the proponents to demonstrate why the burka should be banned, not why it can be banned. Wearing a crucifix around your neck is not an obligatory part of the Catholic faith but the government is not considering banning crucifixes. The burden of proof is on the ban's proponents to demonstrate 'why', not 'why not'. A burka ban may not directly infringe a Muslim's freedom of religion but it undoubtedly infringes their freedom of expression and their right to wear whatever clothes they want to. Whether the burka is an integral part of the religion or not, it is irrelevant. On a civil level, the ban dictates what a woman can and cannot wear. This is an infringement of civil liberties and promotes the repression of women.
[P1] The burka is not a religious requirement, it is customary. [P2] Therefore, a ban would not infringe a Muslim's freedom to practice their religion. [P3] Therefore, there is no reason why it shouldn't be banned.
[Rejecting P3] It may not infringe a Muslim's freedom to practice their religion, but it infringes a woman's right to wear the clothes she feels most comfortable in.