since you live in Turkey and the risks / consequences of getting outed are probably severe, I would encourage you to consider having a designated safe person / friend who can clean & keep the clothes for you, ideally a female friend or a male friend with sisters who can swing that? Are there any LGBT+ groups or centers that you know about where you could maybe connect with people who could help you with these logistics?

I wouldn’t use certain anti-microbial, moisturizing hand soaps for cleaning clothes, but yes - a simple bar soap is probably fine for washing clothes (I have used simple bar soaps to hand-wash my clothes without issue, you just have to be prepared to scrub and rinse them many times to get all the soap out, which incidentally also gets the dirt, sweat, etc. out.)

Don’t underestimate the risk of your parents going through your things when you’re not there, even for reasons you wouldn’t expect. (For example, my parents went through my backpacks and possessions without my knowledge or consent, and then tried to justify it by saying they thought I was abusing drugs, even though I never had used drugs and there was no actual justification or reasoning they could provide for why they thought that, let alone accountability on their end. They also took my private journal - so be careful about what information you write down or leave around - including your lemmy account, etc.)