I totally agree with the conclusion you draw in the opening of your last paragraph: "It feels weird to say that I'm proud of something I didn't get to choose."
I have resonated with that for quite a long time.
I associate pride with accomplishment. I'm proud I graduated from college, got a master's, spent 34 years as a teacher, and any other challenges that I have faced.
As for where I am from, I agree with you: I had nothing to do with it.
And the opposite emotion - shame - is the same for me. So, as for our last president (the one whose name rhymes with "chump"), no, I am not ashamed of anything he did. Those actions are on him, not on me.