Another concern is that telling or suggesting to very young children that they may be the 'wrong' gender can really mess with their minds. Everyone is very concerned about poor little children who are the 'wrong' gender and don't get any help, but we don't hear much about those who are TOLD they are the 'wrong' gender and need to change.
I was told by a well-meaning, desperate-to-be-open-minded-and-supportive youth worker at an early age that I was a lesbian because I wasn't interested in boys. Actually, I was just a late developer and at 11 or 12, boys were still 'yuk' because everything romantic was 'yuk' not because I was interested in girls. This messed with my mind so much, because I worried that I was 'supposed' to feel interested in girls, which I thought was even more 'yuk' than being interested in boys. And when I DID start to develop an interest in the opposite sex, I was worried that I was 'wrong' to do so because I'd been told that I was a lesbian!
I was also a real tomboy, always in trousers, hated skirts, loved climbing trees, playing with trains...I'd often say I wished I was a boy, because boys seemed to have all the fun games and didn't have to wear silly clothes. I'm just very thankful that back then, no one came rushing along to 'support' me in my 'need' for gender reassignment. If it took me that long to recover from being told I was a lesbian, goodness knows how much damage would have been done by telling me I was the wrong gender!
Just let children be children. If any of them have any truly serious issues, this will become evident very quickly and can be dealt with. But adults shouldn't be putting ideas into their heads because it can take years for children to recover from the damage this does.