When you adapt your style to others, it will help you build much better bridges to them. They will respect your approach (because, after all, it’s like theirs). They will trust you more. They will think more highly of you.
In any competitive endeavor, this will give you a winning edge that others might not know about. After all, it's not just what you know. It's not just who you know. It's how others think and feel about you that makes all the difference.