You don't have a "random dice roll of DNA", you have a very specific lineage of DNA passed to you by your parents.
You are the sum of your parents, and a reflection of all of your ancestors before you. I don't see anything irrational with taking pride (or shame) in the ancestral line that resulted in your genetics.
I think the biggest change is online dating. It has constrained the "selection function" to things that can be compressed into a picture and profile text. It may look like it is biased toward certain genes but at the same time it is also wholly incomplete in that regard. You don't even get to hear someone's voice which is purely derived from genetics!
You are the product of your ancestors. What you're saying is like a tree branch saying "I had nothing to do with picking my tree". A tree branch doesn't exist as an isolated individual from the tree and then get randomly assigned to a tree, it only exists because it was created by the tree.
If the tree hadn't created it, then it wouldn't randomly belong to another tree, it just wouldn't exist at all.