Frenemies is a common trope in romance.
I don't believe that extreme enemies can really turn into lovers. There's a reason stalking doesn't work. One can forgive but not forget--unless one is crazy and self-defeating (see abused spouses of either sex)--certain behavior that left one feeling battered and emotionally drained. When every cell in the body declares, "Look out!" only a self-destructive person doesn't listen. And only a masochist climbs back on that horse.
And yet, the frenemies trope offers delightful possibilities: banter, personal revelation, change in attitude, growth, reader surprise.
One possibility is for the "enemies" to be enemies by the demands of culture--rather than by personal dislike or lack of compatibility. One of my favorite yaoi manga series, Rabbit Man Tiger Man, uses this approach. The doctor (rabbit man) is unnerved by his tiger man swain's yakuza ties and boisterous "I'll eat you up" attitude. The doctor, Uzuki, comes across as timid yet he stands up to his rather overwhelming, Rochester-like lover when his ethics override his timidity. And he goes searching for him.
The point of similarity: both the doctor and the policeman WANT to interact with the supposed "enemy." They just aren't sure how, or if they should, or what society will think.
But they embrace the relationship for its own sake. They don't need to make "I loathe you and myself, but I'll keep going back" excuses for the story line to continue.
Quite the opposite. Rather than demoralizing the protagonist, the relationship helps the protagonist thrive. The partner's behavior may be less than civilized. But the protagonist becomes healthier and happier and stronger.
(Whether yakuza have that effect on people in real-life relationships is a separate issue.)
