Like you say, every person's experience is different. In my case, people are so afraid of not being "politically correct" that they're afraid to say anything in case they're being offensive so they take the easier tactic of apologizing then walking away.
Whereas if I casually mention my deafness sometime after the introduction, they had already gotten to know me well enough to know that it's not such an issue to communicate with a deaf person.
Someone raised a question about this one: should we introduce ourselves as "my name is .... and I'm deaf" or should we just be ourselves and normalize it so it's normal for the other person as well?
For instance, scenario 1: i walk into a bakery and say "I'm deaf" before making my order. They kinda freeze. "Oh, we have a DEAF person here. What should we do? Am I going to get in trouble with my boss if I don't act properly? how is one supposed to talk to a deaf person? how do I deal with their "special needs"?" You can see the look of uncertainty and slight panic in their eyes.
Scenario 2: i walk into a bakery and start signing right away for what i want. I point at the food and make the universal gesture for how much? right away, I'm just being myself and normalizing my deafness and they respond, usually, in kind. you can almost see the relief in their eyes like "oh, ok, this person's deaf but no big deal, we can still communicate. Nothing to worry about."