Which of these has the greatest impact on how people obtain their gender identity?

The correct answer is family and friends.

When people obtain their gender identity their family and friends are the groups that impact them the most.

A family is a primary group that has a direct relation with the individual since the beginning of his/her life. The grade of influence is huge. Friends are a secondary group of reference and they play an important role in many aspects of people's lives. That is why these groups are so important for individuals when they obtain their gender identity. They expect the support, love, and comprehension from family members and closest friends.

the atm that sounds like it should be the answer

in an absolute  monarchy, the  monarchrules as an autocrat, with absolutepower  over the state and government — for example, the right to rule by decree, promulgate laws, and impose punishments. the  monarch isnominally sovereign but the electorate, through their legislature, exercise political sovereignty.