In places where transgender people are already allowed to choose the restroom they feel most comfortable with, there has not been a rise in sexual assaults. In Massachusetts, for example, there was no difference in sexual assault rates between cities that allowed it and those that didn’t. 
A similar study undertaken by the UCLA School of Law had similar findings.
The same men proposing these laws under the guise of protecting women are the ones standing by Brett Kavanaugh and President Donald Trump who have both faced serious allegations of sexual assault against women. The appearance of protecting women often only matters when convenient to advocates of these arguments.