Here's the problem in this world, since these girls confronted and accused the boys of something they had no proof of. Therefore, it falls under "nobles law" where if a noble lower than you or a commoner disrespects you, you can take any action you deem necessary to remedy the situation and that supersedes the Taboo Index (which is essentially the absolute law of the land).
Eugeo breaks control of the system as an artificial soul and manages to make himself a "normal person" by realizing how wrong this is by absolutely destroying one of the boys with his sword by cutting his arm off. Thus making him a high criminal and breaking the Taboo Index and before the other boy kills Eugeo, Kirito also highly disgusted with the situation bursts in and saves the other girl and Eugeo by chopping off both the guys arms. Thus, again breaking the Taboo Index and becoming a high criminal.
This picture of him losing his arms is quite satisfying
Now while some people might find it tasteless to use this to progress the plot, they did it in a way to show it off as such a disgusting act that Kirito and Eugeo had no problem taking care of the situation their friends were in by murdering two people. This also helped Eugeo, an artificial soul, break his programming and become "human" but also gave them the opportunity to reconnect with a memory wiped Alice. Basically with both boys taking out the other two by saying "fuck the Taboo Index these girls are our friends and we NEED to help them because this is disgusting" they used this effectively in the plot and touched on it properly.
I felt they did a good job when they used this topic.
And below here it shows that both Kirito and Eugeo have no regrets for helping those two out.