I was actually repeating what was said in a video I watched yesterday so I went to look at their sources - here is a relevant study that supports this conclusion - https://www.sciencedirect.com/science/article/abs/pii/S1743609515339060
However while looking it up in google scholar I did find another study that concluded the opposite, that there’s no significant difference between identical and fraternal twins. That study is here. https://www.nature.com/articles/s41598-022-17749-0
So it’s possible that I was misinformed.
As a bonus, here’s an interesting analysis about what even is gender and gender identity in an academic setting. https://academic.oup.com/analysis/advance-article/doi/10.1093/analys/anad027/7204699
That portion is anecdotal. These stories come from either before there were ethics guidelines in psychology so people were studying their own children, or reviews of child abuse cases where the parent was forcing a different identity on their children. This is not something that is possible to (ethically) run an empirical study on, unfortunately.