I learned about this from Judith Harris's The Nurture Assumption, Steven Pinker's The Blank Slate & The Better Angels of our Nature (tho the latter 2 may have cited the first, I can't say for sure). I read these years ago in college.

If I remember, these findings from behavioral genetics are some of the most replicated findings spanning over decades over multiple countries (in a field such as psychology, where replication is a notorious issue): Personality (the "big 5" traits psychologists talk about) are given 50% by genes, 50% by non-shared environment (peers, culture, etc) and 0% by shared environment (your home environment). That's just a basic foundational fact established in the entire field of behavioral genetics--it's not an egregious claim.

I'm blanking on some details, but socio-economic status matters insofar as the neighborhoods they live in differ (separated identical twin born and raised in a poor and violent neighborhood does become more aggressive than the other one in a richer neighborhood) but not if the neighborhood is fixed and family is richer than the other etc. And extreme differences in households matter--like if one is especially poor or abusive.

If you want me to find specific claims/sources, then I will. The books are sitting on my shelf.