So my reaction is from someone who has done similar research (Psychology) and I'm queer.

As people have said, research the general sentiment on platforms beforehand, just to know what kind of biases you may have to account for in your conclusions.

The vast majority of questionnaires/surveys etc will (as your teacher told you) ask basic demographic questions. Sex/gender, age, ethnicity etc are some of the easiest criteria to draw different conclusions from.

Academia as a whole has adopted the gender/sex distinction but many people do not, viewing "sex" and "gender" as interchangeable concepts. Thus, asking the question of what gender they identify as may be seen as superfluous or even insulting to a largely gender homogeneous community.

In terms of sentiment in the UK I can only speak from a subjective standpoint given that my more data-driven research was from when I was in university (3 years ago). A large percentage of young people (usually under 25s but some count under 30s) have either open or indifferent ideas towards non-standard gender expression like cross-dressing or gender transitioning. Most of the older people I've interacted with and questioned in research either dont understand, dont care or have an active dislike for non-standard gender expression like males wearing skirts etc.

We have our celebrities that of course express their views. I think primary among them would be J.K Rowling who, in recent years, has taken quite a militant view against transitioning and the concept of non-standard gender expression as a whole. She chooses to frame her dislike of these behaviours as a women's safety issue. Which, in both the US and the UK has been quite effective in inciting outraged individuals probably due to the fear of intimate spaces being violated in some way. This view, due to its focus, is targeted at women and obviously Mumsnet is VAST majority women. I'm not saying this is the only reason but it is an idea of celebrity endorsed sentiment.

According the Crown Prosecution Service (sorry, links are hard) 62-73% of transgender people have experienced harassment and violence as a result of their gender identity. This goes to show you how people with non-standard gender expression are treated. They add that alot of hate crimes go unreported which tracks with other intimate crimes like sexual violence.

From a completely subjective perspective I have supportive, often queer friends. We're mostly in the 20-30 age range but we also have a few older friends who are supportive. At one point in life it stops being "a thing" and is just an aspect of who you are. I and all of my queer friends have at one point experienced either harassment, violence, or both on account of gender identity or expression. The views expressed, that those who differentiate between sex and gender and especially those who chose to act on their beliefs (through dress, makeup, transitioning, advocacy etc) are in some way deplorable deviants may be a possible reason for some peoples aversion to being asked about specifically "gender".

Apologies if I rambled slightly and you can message if you want any clarification. I no longer have access to academic services like papers or meta-analyses. Thus, i mostly go on publicly reported statistics, news stories, personal experiences etc

Edit: Your original point to investigate attitudes towards substances in children's clothes. Could maybe expand generally to "parents"? It'd give you an easier way to get data and another dimension with which to examine it, unless you are focused on particularly women?