The APA (?) has published a report  on the sexualization of girls, part of which lists substantial evidence that sexualization and objectification is happening (by both males and females) and getting worse in US culture and other Westernized cultures. These are proven to "undermine confidence in and comfort with one's own body, leading to a host of negative emotional consequences, such as shame, anxiety, and self-disgust."  The three most common mental health problems in girls/women (eating disorders, low self-esteem, and depression) can also be brought on by sexualization.  Self-objectification has been repeatedly shown to cause problems concentrating, focusing attention, and thus impairing mental activities such as math and logic.  Lastly, self-objectification has been linked to sexual problems in adulthood.  These links can be strengthened by the research that shows a link between lack of education and higher rates of teen pregnancy.  Of course, teen pregnancy leads to all sorts of problems for the teen, their offspring, and society as a whole. 
So how can you lead your child away from this path? To start with, be a sexually liberal parent, because children that come from sexually liberal families are more likely to be sexually liberal themselves.  Research shows that children who are exposed to non-sexual nudity develop a positive attitude towards sexuality, which will likely benefit his or her own sexual comfort.  And having more body acceptance and sexual comfort is linked to a decrease in teenage pregnancy. 
It's interesting to note that textilers (?), both children and adults, often dislike their genitals. Nudists, on the other hand, like all body parts somewhat evenly, including the genitals. [6, 7] This supports the evidence that family nudism has a higher correlation to body self-concept than does sex, race, or location.  Also, nudist children have much higher body acceptance and self-image than do non-nudist children.  Non-nudist US children somewhat strongly believe that clothing is required, even in hot climates, but are unable to explain why. 
It seems that nudism is of benefit to children, but you shouldn't believe my bias opinion. Instead, here's a description (from ) from Lawrence Casler, a non-nudist professor and researcher:
"I was able to interview several of these children, in addition to a number of older children who visited Sunshine Village [Nudist Resort] with their parents but were not involved in the children’s camp. For the younger children, nudism chiefly meant nude swimming, having fun without getting one’s clothes dirty, being with friends, etc.
"For the older children, nudism seemed also to have a more serious meaning. These adolescent boys and girls seemed unusually alert and aware of the impact nudism had on their lives. With only one exception, they stated that they would like to be nudists even if their parents were not. In addition to the usual ‘fun’ reasons, many of the teenagers referred to the benefits in mental health and emotional stability.
"Many of them recognized that nudism was giving them a more ‘realistic’ outlook towards sex than their non-nudist friends possessed. When with these friends, or out on dates, they could only feel sorry for people whose attitude towards the human body was not as healthy as their own. Unlike the responses of some adult camp members, these seemed completely genuine and spontaneous. Furthermore, the impression was inescapable that these children, taken as a group, were extraordinarily well-adjusted, happy, and thoughtful."
If that's not enough, here's 205 additional arguments in support of naturism. (25 of which are from the Bible, if that's your thing. It's a recommended read nonetheless.) All I ask is that you consider naturism or at least more liberal attitudes towards nudity and sexuality in your home. Nothing beats personal experience, so here is your invite to find a family friendly nudist resort and give it a try.
What about your children?
Additional comments can be found here.
 Eileen L. Zurbriggen, et. al., "Report of the APA Task Force on the Sexualization of Girls", 2007. Link to the full PDF or HTML summary.
 Joseph P. Allen, et. al., "Preventing Teen Pregnancy and Academic Failure: Experimental Evaluation of a Developmentally Based Approach", Child Development, Vol. 68, No. 4 (Aug., 1997), pp. 729-742. link to the abstract.
 Paul Okami, et. al., "Sexual experiences in early childhood: 18-year longitudinal data from the UCLA family lifestyles project.", The Journal of Sex Research, 9/22/1997. Full text.
 Robin J. Lewis and Louis H. Janda, "The relationship between adult sexual adjustment and childhood experiences regarding exposure to nudity, sleeping in the parental bed, and parental attitudes toward sexuality", Archives of Sexual Behavior, 8/1/1988. Abstract.
 Elise F. Jones, et. al., Teenage Pregnancy in Industrialized Countries, Yale University Press, 1986. Very brief summary.
 Marilyn Story, "Comparisons of Body Self-Concept Between Social Nudists and Nonnudists", The Journal of Psychology, Volume 118, First Half, September 1984, pp. 99-112. Full text.
 Marilyn Story, "Factors associated with more positive body self-concepts in preschool children", The Journal of Social Psychology, 108, 1979, pp 49-56. Summary.
 R. J. Goldman, J. D. Goldman, "Children’s perceptions of clothes and nakedness: a cross-national study", Genetic Psychology Monographs. 104, 1981, pp 163-185. Summary.
 Lawrence Casler, “Some Sociopsychological Observations in a Nudist Camp: A Preliminary Study”, Journal of Social Psychology, 64, 1964, 307–323. Quoted via newsletter.
Appendix A: Comments on finding sources.
I've been working on an academic-style post entitled "What about the children?!" to hopefully boost readership. (Or at least get a decent number of links to the post via news story comments, where others have asked that same question.) The goal is to make a short post that uses logic and solid, non-bias linked references in order to prove that children are not harmed by non-sexual nudity and may even benefit from it. Part of the challenge is a concise delivery of the information, and the other part is the sources. I'm sure that all of you have heard of the "205 arguments for nudity" publication. I think it's great, as I'm sure all of you do too. More to the point, it is extremely convincing. However, I noticed that some of the arguments don't have references. No biggie, as long as I can make good use of some of the other numerous sources listed at the bottom of the publication. (It sounded like a good idea at the time...) It may be convincing, but it's not necessarily true.
Have you ever looked through those sources? They're mostly opinion, which doesn't help in my goal one bit. In fact, good research in this area is somewhat difficult to come by. Even if I find a reference that looks good, it's very challenging to dig up the actual publication! I hate places that charge for papers. (Isn't academia all about the free exchange of information?) For some papers, I'll just have to rely on what I can get: abstracts, summaries, and what others have quoted. Fear not though, as I've dug up some good stuff already and am slowly putting it together. Thanks for being patient with me; patience is a virtue!
Appendix B: Afterthoughts.
The goal was to make a short, non-bias, research-backed response to everyone who asks "What about the children?!" Did I succeed? It wasn't easy -- there just isn't a whole lot of research! Hopefully, the statistical facts can put some sense into the textilers that unknowingly support the sexualization of our culture. Remember people: nudity doesn't equal sex, and an exposed nipple isn't the end of the world.
I used the American tactic: Cause fear, then suggest your intention! Does it work? Do you think you can do better? I'd love to hear suggestions for improvement, because I will likely be editing the post a few times. Let's consider it a rough draft for now.
One issue currently is that it's difficult to differentiate between "sex" and "sexuality". People in the US have trouble separating the two, but I'm not sure what I can do to clarify the terms. "Sexuality" is good for children, and "sex" (and sexual abuse) is bad for children. (There is plenty of research linking sexual abuse with later sexual problems and violence.)
Lastly, a link that I found and wanted to put in the post...but didn't. Apparently there is a book that links tight fitting bra's with breast cancer. I assume the same is true with male undies or tight jeans, which may be a reason for the high rate of infertility. Anyway, that's yet another reason why clothing is bad.
Appendix C: A better version.
A better summary of research has been done by Mark Storey. See Nude & Natural 23.4 (Summer 2004), "Children, Social Nudity and Academic Research".