That's a great question. Here's the advice I wish someone had given me ten years ago:
I would re-establish my relationship first. I would improve my communication with them, bond closely, share good times, etc. And like you have done, I would stop mentioning Islam for awhile.
You can only be as "controversial" as you are close. A strong relationship can handle controversy. A weak relationship will simply break apart with controversy. A semi-strong relationship can withstand a little controversy. So build a strong bond first.
I would also try to think of the person's "stubbornness" in some other way. I would reframe it.
I read a good story of reframing: A father and his daughter had always had arguments and the father thought of his daughter as stubborn. But the meaning and judgment of a behavior at least partly has to do with the context. In the context of disobedience to him, the father thinks of the daughter's behavior as stubborn. But a friend gave him a different view: "Imagine what will happen when the girl is a young teen and a boy is trying to convince her to do something sexual. She will not be easily persuaded. Why? Because she's stubborn."
The different context casts the exact same behavior in a new light. Instead of a negative thing, the stubborn behavior could be seen more positively. Under those circumstances, the father himself might call it something very different: "standing up for herself" or "having integrity" or "hard to manipulate" or "strength of character." He might be proud of his daughter for her behavior.
Do the same thing with the person close to you. Try to think of the behavior you've been calling "stubborn" in a different light, from a different context, and use different words. If you were going to call that behavior something positive, what would it be? This is a way to break down a barrier between the two of you. It is a way of forgiving your friend for resisting you.
And finally, I wouldn't try to convince your friend in one conversation. I would think in terms of small bits and long campaigns. Read more about that here.