If elements of society are concerned about the repressive and patriarchal effect of the burka, they should promote measures to foster constructive public communication and debate on the issue instead of applying legislative action to ban burkas.
A burka ban would instantly fuel resentment from Muslim communities towards the government and those calling for a burka ban. This resentment would shut down public debate on both sides, with Muslims accusing the government of Islamophobia and supporters of the ban accusing British Muslims of harbouring sexist and patriarchal beliefs. For those genuinely concerned about the sexist and patriarchal symbolism inherent in the burka, a blanket ban would be a travesty. It would be highly insensitive of another culture and all but shut down public communication on the issue. Instead, they should seek ways to foster public discourse, promote healthy debate and engage in dialogue about universal values and rights.
Not everything needs to lead to a public debate. Some things that are inherently oppressive or dangerous must be banned without debate. Some elements of society may complain, but it is in the best interests of society as a whole. For example, many libertarians propose that all drugs should be legal. This does not mean that the government should not legislate until the public debate is concluded and one vein of thinking emerges victorious. It should ban dangerous drugs in the interest of public safety until public pressure to do otherwise becomes too loud to ignore. The same applies to the burka. If we accept that the burka promotes gender inequality, the government should take action and ban it in society's best interests. If the public sentiment changes at a later date and the burka is viewed differently, the ban can be lifted. However, in the meantime, it is in the public's interest to ban it.
[P1] A blanket burka ban would shut down public debate. [P2] This would be counterproductive to reducing gender inequality. [P3] Therefore, we shouldn't ban the burka.
Rejecting the premises
[Rejecting P2] It would not be counterproductive to gender inequality.