I used to have a severe stutter, like really bad. I would say top 5 bad. Blockades lasting more than a minute until I just gave up. And I looked horrible when I stuttered, because of all the pushing and struggling. Both myself and the listener would be uncomfortable. Now I'm somewhere between mild and moderate, but most importantly: I do not suffer mentally anymore like I used to. That was the worst part for me. So no, I am not wrong in saying that people will accept you after a while. Experienced this myself so it is possible, making your statement untrue. And it's just how you are, and they will get used to it. You just didn't experience it yet.