If you’re insincere, then that reaction is probably the only reason you’re apologizing.
If you did something wrong, and you need to take steps to make it right, then apologizing is a first step. Whether they accept it or not, that won’t stop you from apologizing.
If they wronged you, but you responded in a bad way, owning your part and apologizing may help you both move forward.
Requiring any kind of response from the other party makes it all about you and how you feel. They may not see things the way you do. They may never come around to your way of thinking, and you may never come around to theirs.
You’re not responsible for their actions or reactions, just your own.