Barely a week goes by without a row over whether women should take their clothes off, keep them on or be allowed to cover up completely. Last week, singer Sinéad O'Connor became the latest to offer a view, writing an open letter to teen sensation Miley Cyrus advising her not to be so frequently or conspicuously naked lest she allow the music business to act as her "pimp".

On university campuses this term, student unions have been attempting to hold back what they see as a tide of casual misogyny by banning Robin Thicke's hit Blurred Lines, with lyrics described by one critic as "rapey".

The campaign to persuade the Sun newspaper to drop its topless models has, by contrast, studiously avoided talk of a ban. No More Page Three wants Rupert Murdoch voluntarily to put the naked "lovelies" out of their misery. Nevertheless, the campaigners have been hampered by many public figures immediately assuming that to voice disapproval of Page 3 might associate them with an illiberal wish to introduce censorship.

Might our nervousness about returning to the days when the lord chamberlain could stride on to the stage to stop an objectionable play have made us too tolerant of publishers, musicians and video game designers who trade in images of women that many find degrading and even dehumanising? Because, for good or ill, the female body and its drapery remains territory where we do battle over our ideas of liberty as well as specific examples of personal choice. "This is a free country," David Cameron asserted last week, promising in the next breath full backing to institutions that wish to forbid Muslim women from wearing the niqab, or full-face veil.

Excessive interference? Or an uncomfortable reminder that the UK's laudable ideal of tolerance and religious freedom has led, in some cases, to moral relativism – a blindness to injustices and injuries that undermine those very freedoms that we cherish, particularly for women. The idea of "a national debate" is often decried as a thin disguise, a veil if you like, to partially conceal intolerant ideas. But in these three very different cases – the still-rare niqab, the daily diet of Page 3 "lovelies", and the monotonously omnipresent naked females in popular music – we should keep the conversation alive about our cultural discomforts.

We applaud Ms O'Connor, the No More Page Three campaigners and Mr Cameron for at least questioning the values of organised religion and commercial entertainment: but no blanket prohibitions, please. Rather, let us have an open discussion – initiated and led by the UK's female citizens, and not merely prompted by some Las Vegas shock merchant making shareable pop videos.

• This article was amended on 8 October 2013. An earlier version said the lord chancellor had the power to censor plays. That was the lord chamberlain's role.