Same. I don't think it's even possible to write a character who has absolutely no similarities with you, unless you're making a caricature/flat character (which is also fine. Not every character in a story have to complex and nuanced), and some life experiences are so universal that no two people would be completely devoid of common ground, regardless of culture and upbringing.
As for myself, I tend write characters & protagonist in with this question in mind: "What kind of journey, developments, and/or self-discovery do I want to see this person go through?"
I've mentioned several times that most of my writing experience came from forum roleplays. I've always loved filling those character creation forms, trying to come up with interesting combinations based on the parameters given by the OP, then seeing how they fare in the world. In that sense, it's kind of like playing a role in a film. I never write deliberate self-inserts, but I might project a lot of myself on them depending on how invested I am in their journey.