”’I’m sorry you feel that way’ is also minimizing. It’s an instant shutdown that lacks empathy for how you may be feeling"
Not a popular viewpoint perhaps, but I have to disagree - in some instances, and I recognize that it's often used as a non-apology.
Sometimes though, rather than being dismissive, this can be a way of actually acknowledging that the other person is upset - (empathy) - without having to agree with them.
Sometimes we're not sorry about what we actually said, but we're sorry that the other person is upset by the words. Saying "I'm sorry I said that" would be disingenuous, and being made to feel like you have to apologize and take the words back is to be manipulated by the other person's reaction.