A minor disagreement can quickly spiral into entrenched conflict.
Soon neither party is willing to concede any point to the other. They won’t work together on any project at any time.
That becomes problematic for any future cohesive efforts
There are two solutions, one is superordinate goals. Establish a goal you both need to work together to resolve. This typically risks being seen as patronising.
Better, flip your opinion. Tell them the other party they are right and you’re wrong. Tell them they've convinced you and you can’t do this without them.
Tell them you respect how much they’ve done and what you like about them, and how hard this debate has been.
Almost every time this occurs, you can salvage a constructive, positive, relationship and get what you need.
If you push too hard to win, you’ll almost certainly lose. If you play to lose, you’ll probably win.