“‘We communicate effectively, talk about our future with pragmatism.’
Now is the time to give it a try. Be realistic here. If you see a future together where you live together/she comes to live with you, you should be able to discuss your different values around cleanliness directly.
‘I am also afraid that this thing might affect our future life as well.’
Well. You should be very afraid. It’s not a question of whether it ‘may’ come or not. You should be afraid that it will definitely be a factor in your life. Is it acceptable to you to live in these conditions every day? That’s what he agrees to.
The parents’ meeting place is the least of your concerns here. The pictures you shared are horrible. She has clearly normalized living in dirty conditions. The fact that she has no problem bringing you into her home in that condition is a clear red flag that needs to be addressed.
I am concerned for you that you would rather feel the discomfort of living in a dirty house, in a dirty kitchen, stepping out of a dirty shower onto a dirty floor where your feet are covered in hair and dirt than feel the discomfort of saying that you refuse to live in their dirty house again.
Tell him directly how you need to have this difficult conversation. Yes, it will feel bad, but his ability to have this incredibly difficult conversation is so important to the health of your continued relationship. You can’t keep silent about this. You can be kind, and you can also be direct.
“I care about you very much, but I want you to know that I was very uncomfortable with the state of your home. I am concerned that you don’t see the problem. Based on the reasons you gave when I offered to clean, you felt it would be futile to try to clean. We need to be on the same page about cleaning in order to move forward toward living together and sharing a home.
Best of luck to you.”
—u/picocure