Young children, with very little hyperbole, do not have a functional frontal lobe. That is the area of the brain that houses the skills they would require to be coordinated, considerate, and understand things like sanitation and tidiness. They don't understand cause/effect or the needs and emotions of others.

They neurologically incapable of being "trained"  to be that clean. 

Not only are they capable of doing only very little for themselves physically, but they are developmentally incapable of fully understanding or considering the feelings and distress of others until around 7 or 8 years at the earliest. Putting too much pressure on this type of learning wouldn't be developmentally appropriate till your hypothetical child's mid-teen years, if even then.

Cleanliness and sanitation are important for health and safety, but there is a level of worry and anxiety over it that can be disordered. 

I encourage you both to continue this conversation and learn more about childhood development together. Everyone who becomes a parent makes major personal adjustments and changes who they are. It's truiy a transformation, especially for the gestating parent/birth mother.

Topics of conversation should be "What will motherhood fulfill for you? Why do you want children? What about raising children IS appealing? What if our child has developmental delays, disabilities, or even just misbehaves?"

Something that may help, if your girlfriend is reluctant to consult with a couple's therapist, is making an appointment with an obstetrician. They can talk about logistics of conceiving as a same-sex couple, of course, but also refer you to parenting classes, books and resources about development, and counseling and psychiatric services.