I'm not sure there is a philosophical answer to this so I can only respond based on my personal experience. I have been interested in human values related issues for many decades, so much so that in my retirement I have chosen to write hard science fiction novellas and short stories about AI based social robots in the near future where the existential and social issues related to human values are the main theme. Fifteen hundred pages to date.
Please read the following with the understanding these are only my opinions, not something I claim to be “the truth”.
You face a daunting challenge because I believe that human values are the basis of our identity. They are the basis of everything we think, say and do. If we took away all your values who would you be? Given this, when our values are challenged it represents an existential danger, a threat, so we defend them at all costs and they are understandably almost impossible to change. Making this more complicated there are values at the species, social and personal levels and some are genetic and some extra-genetic (learned). If someone has personal values at the genetic level (twin studies) you can imagine how hard those will be to change. Given that many advanced psychotherapies attempt to change an individuals values, and yet often fail, consider the task at hand.
I would suggest the best you can do is to come to an understanding of each other’s views. Even acceptance is normally a bridge too far as far as values differences go.
You use the word “duty” and that is also a values related term and subject to philosophical debate in itself so lets put that aside.
One might say you are negotiating with your friend regarding your value differences. At one point in my working life I was involved in negotiations at the corporate level so of course I was sent for training. The two books that are relevant to your question are “Getting To Yes” https://en.wikipedia.org/wiki/Getting_to_Yes and “The 7 Habits of Highly Effective People”. Only the chapter titled “Seek First To Understand, Then To Be Understood” of the 7 Habits book is of interest here.
I was sent to multi-day, out of town training seminars based on these books. Borrow them from the library and have a look if you fee so inclined.
The key thing to notice with regards to these books is that your approach must be structured and you will have to learn how to do that. Because most people listen with the intent to reply they do not listen as empathically or as deeply as they might. “Active Listening” is related skill you might look up and investigate and it will provide you with additional structured methods.
Best of luck.