There are currently over 3000 research papers published worldwide providing evidence that trans women are women, and trans men are men. Here are just a few:

• Evidence Supporting the Biologic Nature of Gender Identity - https://www.sciencedirect.com/science/article/abs/pii/S1530891X20357682
• Endocrine Society Position Statement on Transgender Health – https://www.endocrine.org/advocacy/position-statements/transgender-health
• Beyond X & Y: Chromosomes and Sex Organs - https://scienceline.org/2020/10/beyond-x-y-chromosomes-and-sex-organs/
• The Neuroanatomy of Transgender Identity: Mega-Analytic Findings From the ENIGMA Transgender Persons Working Group - https://www.sciencedirect.com/science/article/abs/pii/S1743609521004252

The bottom line is that trans women are women. To say any different is offensive and biologically incorrect. Once you have that as your base, then which restroom to use becomes simple. A trans women uses the women’s restroom and trans man use the men’s.

If your next argument is to say that trans women are a threat to women in single sex spaces, then you would also be wrong. There is plenty of proper scientific research and evidence proving that they are no threat (see https://link.springer.com/article/10.1007/s13178-018-0335-z for more info). However, it is the case that trans women are more likely to be physically and verbally assaulted (including sexually) than cis women. This is proven from official government data for recorded assaults, which also shows a very worrying increase in attacks - including from cis women.

BTW. Trans is short for transgender. It is a descriptive word. E.g. tall woman or short woman. When you talk about cis, it is also descriptive. All trans women, cis women, tall women, tall overweight women are women.