Is this innocent photo of my daughter inappropriate?

Courtney Adamo certainly thinks so. The 33-year-old has posted more than 1,500 pictures of her four children on her Instagram account.

There's the youngest, Marlow, curled up in her cot. And there she is asleep, again. And again and again. There's everyone in their swimming cossies, sipping orange juice on holiday and – look! – there they are, in the bath, up a tree, and on the beach. Here is a picture of baby Marlow in hospital, "so congested she can barely breathe", and here she is having her first ever bath in the kitchen sink.

But there is a picture of Marlow you won't see on Instagram, and that is the one shown above. The snap was taken down by Instagram, despite the fact that the child was only doing what everyone else on Instagram specialises in: gazing at her own navel.

When Mrs Adamo re-posted it, the social media giant deleted her account completely. "I thought it was such a sweet photo of my baby girl and her gorgeous, round belly (and outie belly button)," wrote Mrs Adamo on her blog. "And I love that her pride is so evident in the photo – such a sweet and innocent shot of a successful day of potty training."

Except Instagram didn't think it was any of those things. A backlash by some of Mrs Adamo's 40,000 followers led to her account being reinstated, though the "offending" picture is still absent. "We try hard to find a good balance between allowing people to express themselves creatively, and having policies in place to protect young children," said a spokesman for the site.

"This is one reason why our guidelines put limitations on nudity, but we recognise that we don't always get it right."

It is estimated that, every day, police forces find thousands indecent images of children online. Some offenders have been caught with more than a million images. In such a world, it seems that even a mother posting a picture of her own child can be censored by social networking sites twitchy about content falling into the wrong hands.

This, then, is the 21st-Century, digital version of the humiliation faced by former newsreader Julia Somerville. In 1995, Somerville and her partner were arrested when a Boots' worker alerted police to pictures the couple had handed in to be developed.

The photos, of her then seven-year-old in the bath, were entirely innocent, but led to the pair being questioned for hours in a police station.

"It was a terrible invasion of our privacy," said Somerville later. "What is difficult to accept is the realisation that the private snaps we all take are not, in fact, private."

It is unlikely that Somerville would have much sympathy for Mrs Adamo and today's crop of socially networked mothers. A survey last year found that the average baby has its picture uploaded on Facebook within 57.9 minutes of being born. I waited an almost eternal five days, but now bore my friends with photos of my daughter at least twice a week. Speaking of which, illustrating this article is an Instagram picture of my child post-bath, although I would never post one of her in the bath, or naked. Those are simply my personal boundaries.

But I don't have a problem if, as happens often, a six-month-old's bottom appears in my feed.

We are in a nasty place indeed if photos of babies in nappies are seen as fodder for perverts and paedophiles, rather than just sweet snaps to share with friends, family – and your 40,000 Instagram followers.

At nurseries and schools, parents are now routinely banned from taking photographs, or even taking their smartphones into the classroom, lest someone takes a sneaky snap of a child running around. At a baby-massage class I took my then six-week-old child to, mothers who wanted to take pictures of their offspring first had to ask the permission of the entire class. "Do you mind if I take a snap of my own daughter?" I asked. "I promise I'm not a paedophile!" Nobody laughed.

Alice Langley is a mother-of-two who blogs for Digital Diaries, a website that explores how technology is changing childhood and parenting. She thinks the real danger isn't unknown perverts making off with digital snaps of our kids – it's us becoming too protective of our children.

"I don't like the idea that posting a picture of your child is somehow exploiting them. I can't police the private thoughts of everyone, or spend my time treading on eggshells because of hypothetical dangers. I let my children be seen in their swimsuits on the beach, but I can't go around checking whether or not everyone who can see them is having inappropriate thoughts."

Alison Perry runs Notanothermummyblog.com and says she will never post a picture of her three-year-old daughter online. "She is her own person," Alison says. "Just because she is too young to make a choice, that doesn't mean I should take the choice away from her.

"Courtney [Adamo] said she set up her Instagram to be able to share the pictures with her family, but I don't see why she couldn't have done that on a private Flickr page. I think it's a lovely picture and it is completely innocent, but it could be taken by anyone and we have no idea where these images end up."

Perry doesn't ban others from putting pictures of her child on social-networking sites, but many do. Lizzie Post, the great-great-granddaughter of American etiquette expert Emily Post, says everyone should ask the parents' permission before uploading a picture of someone else's child. "People have digital boundaries for their families and it's important to respect them."

Is this all a little too much? Siobhan Freegard, who runs Netmums, thinks the fact that Instagram is moderating itself can only be a good thing. "It's a cute little picture," she says of Mrs Adamo's snap. "There is obviously nothing sexual about it, and anyone who thinks there is is clearly sick in themselves.

"It does seem strange that they would take it down when you can freely see bum cheeks and breasts everywhere else. But they are trying to police themselves, which is more than can be said for other sites. I respect that they are trying to keep their site clean. Given the size of it, it seems inevitable that they will make the odd mistake."

And that gets to the heart of this very 21st-Century issue. Because however sweet and pure the picture of baby Marlow is, in the battle for a safer internet wouldn't we rather innocent pictures were taken down than inappropriate ones left up?