Assuming she was telling the truth during this chapter the MC did have the 100% correct and moral response to her story and her diatribe is just her continuing to spiral out of control due to her situation and he definitely should not enable that spiraling no matter how grippy the socks and other things are.
Because she didn't say something like "Oh Me and my Mom had a bad fight over homework can I crash at your apartment for 176 chapters or so until we fall in love and start dating?" She said "My Mom makes Underage Porn of me without my consent and today she brought over a guy and they attempted to rape me in the shower." and, assuming they aren't in one of the crapsack dimensions where the only solution is a downward spiral into murder-suicide, the correct response to that is, "We should Call The Police and Child Protective Services", not "Oh you can crash at my place for a few days until the situation calms down".
That is not a situation that "Calms Down".